US RE38476 E1 Abstract The present invention involves method and apparatus for analyzing two measured signals that are modeled as containing primary and secondary portions. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, the present invention involves utilizing a transformation which evaluates a plurality of possible signal coefficients in order to find appropriate coefficients. Alternatively, the present invention involves using statistical functions or Fourier transform and windowing techniques to determine the coefficients relating to two measured signals. Use of this invention is described in particular detail with respect to blood oximetry measurements.
Claims(28) 1. A system for the enhancement of physiological signals for the measurement of blood oxygen in a subject, the system comprising:
first and second light sources to direct light toward the subject, said first and second light sources producing light of first and second wavelengths, respectively;
a light detector positioned to detect first and second light signals after interacting with the subject and to generate signals indicative of an intensity of said first and second detected light signals, said first detected signal having a first portion arising from light transmitted from said first source and a second portion arising from a first interference source, said second detected signal having a first portion arising from light transmitted from said second source and a second portion arising from a second interference source;
a storage location containing a mathematical relationship of said first and second portions of said first and second detected signals and a first ratio of said first portion of said first detected signal to said first portion of said second detected signal;
an analyzer coupled to said storage location to determine a plurality of possible values for said mathematical relationship over a predetermined range of said first ratio; and
a calculator to determine a selected value from said plurality of possible values for said first ratio based on said plurality of values.
2. The system of
3. The system of
4. The system of
5. The system of
6. The system of
_{a}(t) and S_{a}(t)−ωS_{b}(t) where S_{a}(t) is said first detected signal, S_{b}(t) is said second detected signal, and at ω is a variable defined over a predetermined range.7. The system of
8. The system of
9. The system of
10. A system for the enhancement of physiological signals representative of a physiological phenomenon characteristic in a subject body tissue carrying pulsing blood, the system comprising:
a sensor configured to be positioned in proximity with the subject body tissue to detect physiological signals and to generate signals indicative of said detected physiological signals when positioned in proximity with the subject body tissue, said detected signals having a first portion arising from the physiological phenomenon characteristic and a second portion arising from an interference source;
an analyzer to analyze and determine a value for from said generated signals, said value being indicative of complications of said generated signals; and
a processor, responsive to said value, to generate a processed signal.
11. The system of
12. The system of
13. The system of
14. The system of
15. The system of
16. The system of
17. The system of
18. The system of
19. The system of
20. The system of
21. A method for enhancement of physiological signals for the measurement of blood oxygen in a subject, the method comprising the steps of:
producing light of first and second wavelengths;
directing light of said first and second wavelengths toward the subject;
detecting first and second light signals after interacting with the subject and generating signals indicative of an intensity of said first and second detected light signals, said first detected signal having a first portion arising from light transmitted with said first wavelength and a second portion arising from a first interference source, said second detected signal having a first portion arising from light transmitted with said second wavelength and a second portion arising from a second interference source;
analyzing said first and second detected signals using a mathematical relationship of said first and second portions of said first and second detected signals and a first ratio of said first portion of said first detected signal to said first portion of said second detected signal to determine a plurality of possible values for said mathematical relationship over a predetermined range of said first ratio; and
determining a selected value from said plurality of possible values for said first ratio based on said plurality of values.
22. The method of
23. The method of
24. The method of
25. A method for the enhancement of physiological measurements in a subject, the method comprising the steps of:
using a plurality of light sources, each producing light of a different predetermined wavelength;
directing light of said predetermined wavelengths toward the subject;
detecting a plurality of light signals after interacting with the subject and generating signals indicative of an intensity of said plurality of detected light signals, each of said detected signals having a first portion arising from light transmitted with one of said predetermined wavelength and a second portion arising from an interference source;
analyzing said plurality of detected signals using a mathematical relationship of said first and second portions of said plurality of detected signals and a first ratio of said first portion of a first of said plurality of detected signals to said first portion of a second of said plurality of detected signals to determine a plurality of possible values for said mathematical relationship over a predetermined range of said first ratio; and
determining a selected value from said plurality of possible values for said first ratio based on said plurality of values.
26. The method of
27. A method for the enhancement of physiological signals representative of a physiological phenomenon characteristic in a subject body tissue carrying pulsing blood, the method comprising the steps of:
positioning a sensor in proximity with the subject body tissue to detect physiological signals and to generate signals indicative of said detected physiological signals, said detected signals having a first portion arising from the physiological phenomenon characteristic and a second portion arising from an interference source;
analyzing said generated signals to determine a value for from said generated signals, said value being indicative of complications of said generated signals; and
processing said generated signals using said value to generate processed signals.
28. The method of
Description This is a continuation of application of U.S. patent application Ser. No. 08/859,837 filed May 16, 1997, now U.S. Pat. No. 1. Field of the Invention The present invention relates to the field of signal processing. More specifically, the present invention relates to the processing of measured signals, containing a primary signal portion and a secondary signal portion, for the removal or deviation of either the primary or secondary signal portion when little is known about either of these components. More particularly, the present invention relates to modeling the measured signals in a novel way which facilitates minimizing the correlation between the primary signal portion and the secondary signal portion in order to produce a primary and/or secondary signal. The present invention is especially useful for physiological monitoring systems including blood oxygen saturation systems. 2. Description of the Related Art Signal processors are typically employed to remove or derive either the primary or secondary signal portion from a composite measured signal including a primary signal portion and a secondary signal portion. For example, a composite signal may contain noise and desirable portions. If the secondary signal portion occupies a different frequency spectrum than the primary signal portion, then conventional filtering techniques such as low pass, band pass, and high pass filtering are available to remove or derive either the primary or the secondary signal portion from the total signal. Fixed single or multiple notch filters could also be employed if the primary and/or secondary signal portion(s) exist at a fixed frequency(s). It is often the case that an overlap in frequency spectrum between the primary and secondary signal portions exists. Complicating matters further, the statistical properties of one or both of the primary and secondary signal portions change with time. In such cases, conventional filtering techniques are ineffective in extracting either the primary or secondary signal. If, however, a description of either the primary or secondary signal portion can be derived, correlation canceling, such as adaptive noise canceling, can be employed to remove either the primary or secondary signal portion of the signal isolating the other portion. In other words, given sufficient information about one of the signal portions, that signal portion can be extracted. Conventional correlation cancelers, such as adaptive noise cancelers, dynamically change their transfer function to adapt to and remove portions of a composite signal. However, correlations cancelers require either a secondary reference or a primary reference which correlates to either the secondary signal portion only or the primary signal portion only. For instance, for a measured signal containing noise and desirable signal, the noise can be removed with a correlation canceler if a noise reference is available. This is often the case. Although the amplitude of the reference signals are not necessarily the same as the amplitude of the corresponding primary or secondary signal portions, they have a frequency spectrum which is similar to that of the primary or secondary signal portions. In many cases, nothing or very little is known about the secondary and/or primary signal portions. One area where measured signals comprising a primary signal portion and a secondary signal portion about which no information can easily be determined is physiological monitoring. Physiological monitoring generally involves measured signals derived from a physiological system, such as the human body. Measurements which are typically taken with physiological monitoring systems include electrocardiographs, blood pressure, blood gas saturation (such as oxygen saturation), capnographs, other blood constituent monitoring, heart rate, respiration rate, electroencephalograph (EEG) and depth of anesthesia, for example. Other types of measurements include those which measure the pressure and quantity of a substance within the body such as cardiac output, venous oxygen saturation, arterial oxygen saturation, bilirubin, total hemoglobin, breathalyzer testing, drug testing, cholesterol testing, glucose testing, extra vasation, and carbon dioxide testing, protein testing, carbon monoxide testing, and other in-vivo measurements, for example. Complications arising in these measurements are often due to motion of the patient, both external and internal (muscle movement, vessel movement, and probe movement, for example), during the measurement process. Many types of physiological measurements can be made by using the known properties of energy attenuation as a selected form of energy passes through a medium. A blood gas monitor is one example of a physiological monitoring system which is based upon the measurement of energy attenuated by biological tissues or substances. Blood gas monitors transmit light into the test medium and measure the attenuation of the light as a function of time. The output signal of a blood gas monitor which is sensitive to the arterial blood flow contains a component which is a waveform representative of the patient's arterial pulse. This type of signal, which contains a component related to the patient's pulse, is called a plethysmographic wave, and is shown in FIG. 1 as curve s. Plethysmographic waveforms are used in blood gas saturation measurements. As the heart beats, the amount of blood in the arteries increases and decreases, causing increases and decreases in energy attenuation, illustrated by the cyclic wave s in FIG. Typically, a digit such as a finger, an ear lobe, or other portion of the body where blood flows close to the skin, is employed as the medium through which light energy is transmitted for blood gas attenuation measurements. The finger comprises skin, fat, bone, muscle, etc., shown schematically in FIG. 2, each of which attenuates energy incident on the finger in a generally predictable and constant manner. However, when fleshy portions of the finger are compressed erratically, for example by motion of the finger, energy attenuation becomes erratic. An example of a more realistic measured waveform S is shown in FIG. 3, illustrating the effect of motion. The primary plethysmographic waveform portion of the signal s is the waveform representative of the pulse, corresponding to the sawtooth-like pattern wave in FIG. A pulse oximeter is a type of blood gas monitor which non-invasively measures the arterial saturation of oxygen in the blood. The pumping of the heart forces freshly oxygenated blood into the arteries causing greater energy attenuation. As well understood in the art, the arterial saturation of oxygenated blood may be determined from the depth of the valleys relative to the peaks of two plethysmographic waveforms measured at separate wavelengths. Patient movement introduces motion artifacts to the composite signal as illustrated in the plethysmographic waveform illustrated in FIG. This invention provides improvements upon the methods and apparatus disclosed in U.S. patent application Ser. No. 08/132,812, filed Oct. 6, 1993, entitled Signal Processing Apparatus, which earlier application has been assigned to the assignee of the instant application. The present invention involves several different embodiments using the novel signal model in accordance with the present invention to isolate either a primary signal portion or a secondary signal portion of a composite measured signal. In one embodiment, a signal processor acquires a first measured signal and a second measured signal that is correlated to the first measured signal. The first signal comprises a first primary signal portion and a first secondary signal portion. The second signal comprises a second primary signal portion and a second secondary signal portion. The signals may be acquired by propagating energy through a medium and measuring an attenuated signal after transmission or reflection. Alternatively, the signals may be acquired by measuring energy generated by the medium. In one embodiment, the first and second measured signals are processed to generate a secondary reference which does not contain the primary signal portions from either of the first or second measured signals. This secondary reference is correlated to the secondary signal portion of each of the first and second measured signals. The secondary reference is used to remove the secondary portion of each of the first and second measured signals via a correlation canceler, such as an adaptive noise canceler. The correlation canceler is a device which takes a first and second input and removes from the first input all signal components which are correlated to the second input. Any unit which performs or nearly performs this function is herein considered to be a correlation canceler. An adaptive correlation canceler can be described by analogy to a dynamic multiple notch filter which dynamically changes its transfer function in response to a reference signal and the measured signals to remove frequencies from the measured signals that are also present in the reference signal. Thus, a typical adaptive correlation canceler receives the signal from which it is desired to remove a component and receives a reference signal of the undesired portion. The output of the correlation canceler is a good approximation to the desired signal with the undesired component removed. Alternatively, the first and second measured signals may be processed to generate a primary reference which does not contain the secondary signal portions from either of the first or second measured signals. The primary reference may then be used to remove the primary portion of each of the first and second measured signals via a correlation canceler. The output of the correlation canceler is a good approximation to the secondary signal with the primary signal removed and may be used for subsequent processing in the same instrument or an auxiliary instrument. In this capacity, the approximation to the secondary signal may be used as a reference signal for input to a second correlation canceler together with either the first or second measured signals for computation of, respectively, either the first or second primary signal portions. Physiological monitors can benefit from signal processors of the present invention. Often in physiological measurements a first signal comprising a first primary portion and a first secondary portion and a second signal comprising a second primary portion and a second secondary portion are acquired. The signals may be acquired by propagating energy through a patient's body (or a material which is derived from the body, such as breath, blood, or tissue, for example) or inside a vessel and measuring an attenuated signal after transmission or reflection. Alternatively, the signal may be acquired by measuring energy generated by a patient's body, such as in electrocardiography. The signals are processed via the signal processor of the present invention to acquire either a secondary reference or a primary reference which is input to a correlation canceler, such as an adaptive noise canceler. One physiological monitoring apparatus which benefits from the present invention is a monitoring system which determines a signal which is representative of the arterial pulse, called a plethysmographic wave. This signal can be used in blood pressure calculations, blood constituent measurements, etc. A specific example of such a use is in pulse oximetry. Pulse oximetry involves determining the saturation of oxygen in the blood. In this configuration, the primary portion of the signal is the arterial blood contribution to attenuation of energy as it passes through a portion of the body where blood flows close to the skin. The pumping of the heart causes blood flow to increase and decrease in the arteries in a periodic fashion, causing periodic attenuation wherein the periodic waveform is the plethysmographic waveform representative of the arterial pulse. The secondary portion is noise. In accordance with the present invention, the measured signals are modeled such that this secondary portion of the signal is related to the venous blood contribution to attenuation of energy as it passes through the body. The secondary portion also includes artifacts due to patient movement which causes the venous blood to flow in an unpredictable manner, causing unpredictable attenuation and corrupting the otherwise periodic plethysmographic waveform. Respiration also causes the secondary or noise portion to vary, although typically at a lower frequency than the patients pulse rate. Accordingly, the measured signal which forms a plethysmographic waveform is modeled in accordance with the present invention such that the primary portion of the signal is representative of arterial blood contribution to attenuation and the secondary portion is due to several other parameters. A physiological monitor particularly adapted to pulse oximetry oxygen saturation measurement comprises two light emitting diodes (LED's) which emit light at different wavelengths to produce first and second signals. A detector registers the attenuation of the two different energy signals after each passes through an absorptive media, for example a digit such as a finger, or an earlobe. The attenuated signals generally comprise both primary (arterial attenuator) and secondary (noise) signal portions. A static filtering system, such as a bandpass filter, removes a portion of the secondary signal which is outside of a known bandwidth of interest, leaving an erratic or random secondary signal portion, often caused by motion and often difficult to remove, along with the primary signal portion. A processor in accordance with one embodiment of the present invention removes the primary signal portions from the measured signals yielding a secondary reference which is a combination of the remaining secondary signal portions. The secondary reference is correlated to both of the secondary signal portions. The secondary reference and at least one of the measured signals are input to a correlation canceler, such as an adaptive noise canceler, which removes the random or erratic portion of the secondary signal. This yields a good approximation to a primary plethysmographic signal as measured at one of the measured signal wavelengths. As is known in the art, quantitative measurements of the amount of oxygenated arterial blood in the body can be determined from the plethysmographic signal in a variety of ways. The processor of the present invention may also remove the secondary signal portions from the measured signals yielding a primary reference which is a combination of the remaining primary signal portions. The primary reference is correlated to both of the primary signal portions. The primary reference and at least one of the measured signals are input to a correlation canceler which removes the primary portions of the measured signals. This yields a good approximation to the secondary signal at one of the measured signal wavelengths. This signal may be useful for removing secondary signals from an auxiliary instrument as well as determining venous blood oxygen saturation. In accordance with the signal model of the present invention, the two measured signals each having primary and secondary signal portions can be related by coefficients. By relating the two equations with respect to coefficients defined in accordance with the present invention, the coefficients provide information about the arterial oxygen saturation and about the noise (the venous oxygen saturation and other parameters). In accordance with this aspect of the present invention, the coefficients can be determined by minimizing the correlation between the primary and secondary signal portions as defined in the model. Accordingly, the signal model of the present invention can be utilized in many ways in order to obtain information about the measured signals as will be further apparent in the detailed description of the preferred embodiments. One aspect of the present invention is a method for use in a signal processor in a signal processor for processing at least two measured signals S
where s
and where r The method comprises a number of steps. A value of coefficient r In one embodiment, the clean signal is displayed on a display. In another embodiment, wherein the first and second signals are physiological signals, the method further comprises the step of processing the clean signal to determine a physiological parameter from the first or second measured signals. In one embodiment, the parameter is arterial oxygen saturation. In another embodiment, the parameter is an ECG signal. In yet another embodiment, wherein the first portion of the measured signals is indicative of a heart plethysmographic, the method further comprises the step of calculating the pulse rate. Another aspect of the present invention involves a physiological monitor. The monitor has a first input configured to receive a first measured signal S
where s
and where r The monitor further has a scan reference processor, the scan reference processor responds to a plurality of possible values for r In one embodiment, the plurality of possible values correspond to a plurality of possible values for a selected blood constituent. In one embodiment the, the selected blood constituent is arterial blood oxygen saturation. In another embodiment, the selected blood constituent is venous blood oxygen saturation. In yet another embodiment, the selected blood constituent is carbon monoxide. Another aspect of the present invention involves a physiological monitor. The monitor has a first input configured to receive a first measured signal S
where s
and where r A transform module is responsive to the first and the second measured signals and responsive to a plurality of possible values for r FIG. 1 illustrates an ideal plethysmographic waveform. FIG. 2 schematically illustrates a typical finger. FIG. 3 illustrates a plethysmographic waveform which includes a motion-induced erratic signal portion. FIG. 4a illustrates a schematic diagram of a physiological monitor to compute primary physiological signals. FIG. 4b illustrates a schematic diagram of a physiological monitor to compute secondary signals. FIG. 5a illustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute primary physiological signals. FIG. 5b illustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute secondary motion artifact signals. FIG. 5c illustrates the transfer function of a multiple notch filter. FIG. 6a illustrates a schematic of absorbing material comprising N constituents within the absorbing material. FIG. 6b illustrates another schematic of absorbing material comprising N constituents, including one mixed layer, within the absorbing material. FIG. 6c illustrates another schematic of absorbing material comprising N constituents, including two mixed layers, within the absorbing material. FIG. 7a illustrates a schematic diagram of a monitor, to compute primary and secondary signals in accordance with one aspect of the present invention. FIG. 7b illustrates the ideal correlation canceler energy or power output as a function of the signal coefficients r FIG. 7c illustrates the non-ideal correlation canceler energy or power output as a function of the signal coefficients r FIG. 8 is a schematic model of a joint process estimator comprising a least-squares lattice predictor and a regression filter. FIG. 8a is a schematic model of a joint process estimator comprising a QRD least-squares lattice (LSL) predictor and a regression filter. FIG. 9 is a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in FIG. FIG. 9a is a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in FIG. FIG. 10 is a schematic model of a joint process estimator with a least-squares lattice predictor and two regression filters. FIG. 10a is a schematic model of a joint process estimator with a QRD least-squares lattice predictor and two regression filters. FIG. 11 is an example of a physiological monitor in accordance with the teachings of one aspect of the present invention. FIG. 11a illustrates an example of a low noise emitter current driver with accompanying digital to analog converter. FIG. 12 illustrates the front end analog signal conditioning circuitry and the analog to digital conversion circuitry of the physiological monitor of FIG. FIG. 13 illustrates further detail of the digital signal processing circuitry of FIG. FIG. 14 illustrates additional detail of the operations performed by the digital signal processing circuitry of FIG. FIG. 15 illustrates additional detail regarding the demodulation module of FIG. FIG. 16 illustrates additional detail regarding the decimation module of FIG. FIG. 17 represents a more detailed block diagram of the operations of the statistics module of FIG. FIG. 18 illustrates a block diagram of the operations of one embodiment of the saturation transform module of FIG. FIG. 19 illustrates a block diagram of the operation of the saturation calculation module of FIG. FIG. 20 illustrates a block diagram of the operations of the pulse rate calculation module of FIG. FIG. 21 illustrates a block diagram of the operations of the motion artifact suppression module of FIG. FIG. 21a illustrates an alternative block diagram for the operations of the motion artifact suppression module of FIG. FIG. 22 illustrates a saturation transform curve in accordance with the principles of the present invention. FIG. 23 illustrates a block diagram of an alternative embodiment to the saturation transform in order to obtain a saturation value. FIG. 24 illustrates a histogram saturation transform in accordance with the alternative embodiment of FIG. FIGS. 25A-25C illustrate yet another alternative embodiment in order to obtain the saturation. FIG. 26 illustrates a signal measured at a red wavelength λa=λred=660 nm for use in a processor of the present invention for determining the secondary reference n′(t) or the primary reference s′(t) and for use in a correlation canceler. The measured signal comprises a primary portion s FIG. 27 illustrates a signal measured at an infrared wavelength λb=λ FIG. 28 illustrates the secondary reference n′(t) determined by a processor of the present invention. FIG. 29 illustrates a good approximation s″ FIG. 30 illustrates a good approximation s″ FIG. 31 depicts a set of 3 concentric electrodes, i.e., a tripolar electrode sensor, to derive electrocardiography (ECG) signals, denoted as S The present invention involves a system which utilizes first and second measured signals that each contain a primary signal portion and a secondary signal portion. In other words, given a first and second composite signals S The system of the present invention is particularly useful where the primary and/or secondary signal portion n(t) may contain one or more of a constant portion, a predictable portion, an erratic portion, a random portion, etc. The primary signal approximation s″(t) or secondary signal approximation n″(t) is derived by removing as many of the secondary signal portions n(t) or primary signal portions s(t) from the composite signal S(t) as possible. The remaining signal forms either the primary signal approximation s″(t) or secondary signal approximation n″(t), respectively. The constant portion and predictable portion of the secondary signal n(t) are easily removed with traditional filtering techniques, such as simple subtraction, low pass, band pass, and high pass filtering. The erratic portion is more difficult to remove due to its unpredictable nature. If something is known about the erratic signal, even statistically, it could be removed, at least partially, from the measured signal via traditional filtering techniques. However, often no information is known about the erratic portion of the secondary signal n(t). In this case, traditional filtering techniques are usually insufficient. In order to remove the secondary signal n(t), a signal model in accordance with the present invention is defined as follows for the first and second measured signals S where s In accordance with one aspect of the present invention, this signal model is used in combination with a correlation canceler, such as an adaptive noise canceler, to remove or derive the erratic portion of the measured signals. Generally, a correlation canceler has two signal inputs and one output. One of the inputs is either the secondary reference n′(t) or the primary reference s′(t) which are correlated, respectively, to the secondary signal portions n(t) and the primary signal portions s(t) present in the composite signal S(t). The other input is for the composite signal S(t). Ideally, the output of the correlation canceler s″(t) or n″(t) corresponds, respectively, to the primary signal s(t) or the secondary signal n(t) portions only. Often, the most difficult task in the application of correlation cancelers is determining the reference signals n′(t) and s′(t) which are correlated to the secondary n(t) and primary s(t) portions, respectively, of the measured signal S(t) since, as discussed above, these portions are quite difficult to isolate from the measured signal S(t). In the signal processor of the present invention, either a secondary reference n′(t) or a primary reference s′(t) is determined from two composite signals measured simultaneously, or nearly simultaneously, at two different wavelengths, λa and λb. A block diagram of a generic monitor incorporating a signal processor according to the present invention, and a correlation canceler is shown in FIGS. 4a and 4b. Two measured signals, S The signals S In one embodiment, an adaptive noise canceler The adaptive noise canceler The adaptive noise canceler FIG. 5c illustrates an exemplary transfer function of a multiple notch filter. The notches, or dips in the amplitude of the transfer function, indicate frequencies which are attenuated or removed when a signal passes through the notch filter. The output of the notch filter is the composite signal having frequencies at which a notch is present removed. In the analog to an adaptive noise canceler The adaptive noise canceler One algorithm which may be used for the adjustment of the transfer function of the internal processor Adaptive processors An explanation which describes how the reference signals n′(t) and s′(t) may be determined follows. A first signal is measured at, for example, a wavelength λa, by a detector yielding a signal S
where s A similar measurement is taken simultaneously, or nearly simultaneously, at a different wavelength, λb, yielding:
Note that as long as the measurements, S To obtain the reference signals n′(t) and s′(t), the measured signals S
In accordance with the inventive signal model of the present invention, these proportionality relationships can be satisfied in many measurements, including but not limited to absorption measurements and physiological measurements. Additionally, in accordance with the signal model of the present invention, in most measurements, the proportionality constants r
s Multiplying equation (2) by r
a non-zero which is correlated to each secondary signal portion n Multiplying equation (2) by r
a non-zero signal which is correlated to each of the primary signal portions s Correlation canceling is particularly useful in a large number of measurements generally described as absorption measurements. An example of an absorption type monitor which can advantageously employ correlation canceling, such as adaptive noise canceling, based upon a reference n′(t) or s′(t) determined by a processor of the present invention is one which determines the concentration of an energy absorbing constituent within an absorbing material when the material is subject to change. Such changes can be caused by forces about which information is desired or primary, or alternatively, by random or erratic secondary forces such as a mechanical force on the material. Random or erratic interference, such as motion, generates secondary components in the measured signal. These secondary components can be removed or derived by the correlation canceler if a suitable secondary reference n′(t) or primary reference s′(t) is known. A schematic N constituent absorbing material comprising a container Initially transforming the signal by taking the natural logarithm of both sides and manipulating terms, the signal is transformed such that the signal components are combined by addition rather than multiplication, i.e.: where I When the material is not subject to any forces which cause change in the thicknesses of the layers, the optical path length of each layer, x The correlation canceler may selectively remove from the composite signal, measured after being transmitted through or reflected from the absorbing material, either the secondary or the primary signal components caused by forces which perturb or change the material differently from the forces which perturbed or changed the material to cause respectively, either the primary or secondary signal component. For the purposes of illustration, it will be assumed that the portion of the measured signal which is deemed to be the primary signal s It is often the case that the total perturbation affecting the layers associated with the secondary signal components is caused by random or erratic forces. This causes the thickness of layers to change erratically and the optical path length of each layer, x The correlation canceler utilizes either the secondary reference n′(t) or the primary reference s′(t) determined from two substantially simultaneously measured signals S Further transformations of the signals are the proportionality relationships in accordance with the signal model of the present invention defining r
where
It is often the case that both equations (12) and (13) can be simultaneously satisfied. Multiplying equation (11) by r Multiplying equation (11) by r A sample of either the secondary reference n′(t) or the primary reference s′(t), and a sample of either measured signal S
or
As discussed previously, the absorption coefficients are constant at each wavelength λa and λb and the thickness of the primary signal component, x Referring to FIG. 6b, another material having N different constituents arranged in layers is shown. In this material, two constituents A Often it is desirable to find the concentration or the saturation, i.e., a percent concentration, of one constituent within a given thickness which contains more than one constituent and is subject to unique forces. A determination of the concentration or the saturation of a constituent within a given volume may be made with any number of constituents in the volume subject to the same total forces and therefore under the same perturbation or change. To determine the saturation of one constituent in a volume comprising many constituents, as many measured signals as there are constituents which absorb incident light energy are necessary. It will be understood that constituents which do not absorb light energy are not consequential in the determination of saturation. To determine the concentration, as many signals as there are constituents which absorb incident light energy are necessary as well as information about the sum of concentrations. It is often the case that a thickness under unique motion contains only two constituents. For example, it may be desirable to know the concentration or saturation of A It is also often the case that there may be two or more thicknesses within a medium each containing the same two constituents but each experiencing a separate motion as in FIG. where signals n Any signal portions whether primary or secondary, outside of a known bandwidth of interest, including the constant undesired secondary signal portion resulting from the generally constant absorption of the constituents when not under perturbation, should be removed to determine an approximation to either the primary signal or the secondary signal within the bandwidth of interest. This is easily accomplished by traditional band pass filtering techniques. As in the previous example, it is often the case that the total perturbation or change affecting the layers associated with the secondary signal components is caused by random or erratic forces, causing the thickness of each layer, or the optical path length of each layer, x One method for determining reference signals s′(t) or n′(t) from the measured signals S
are substantially constant over many samples of the measured signals S The constant saturation assumption is equivalent to assuming that:
since the only other term in equations (23a) and (23b) is a constant, namely the numeral 1. Using this assumption, the proportionality constants r In accordance with the present invention, it is often the case that both equations (26) and (30) can be simultaneously satisfied to determine the proportionality constants r Multiplying equation (19) by r
Multiplying equation (19) by r
When using the constant saturation method in patient monitoring, initial proportionality coefficients can be determined as further explained below. It is not necessary for the patient to remain motionless even for an initialization period. With values for the proportionality coefficients r In accordance with one aspect of the present invention, the reference processor
for r=r In order to determine either the primary reference s′(t) or the secondary reference n′(t) from the above plurality of reference signals of equation (32), signal coefficients r
In other words, coefficients r One approach to determine the signal coefficients r Use of a plurality of coefficients in the processor of the present invention in conjunction with a correlation canceler
With properties (1), (2) and (3) it is easy to demonstrate that the energy or power output of a correlation canceler with a first input which corresponds to one of the measured signals S
where j=1, 2, . . . , n and we have used the expressions
The use of property (3) allows one to expand equation (35) into two terms so that upon use of properties (1) and (2) the correlation canceler output is given by
where δ(x) is the unit impulse function
The time variable, t, of the correlation canceler output C(S It should be understood that one could, equally well, have chosen the measured signal S It should also be understood that in practical situations the use of discrete time measurement signals may be employed as well as continuous time measurement signals. A system which performs a discrete transform (e.g., a saturation transform in the present example) in accordance with the present invention is described with reference to FIGS. 11-22. In the event that discrete time measurement signals are used, integration approximation method such as the trapezoid rule, midpoint rule, Tick's rule, Simpson's approximation or other techniques may be used to compute the correlation canceler energy or power output. In the discrete time measurement signal case, the energy output of the correlation canceler may be written, using the trapezoid rule, as where t The energy functions given above, and shown in FIG. 7b, indicate that the correlation canceler output is usually zero due to correlation between the measured signal S It should be understood that there may be instances in time when either the primary signal portions s Since there may be more than one signal coefficient value which provides maximum correlation canceler energy or power output, an ambiguity may arise. It may not be immediately obvious which signal coefficient together with the reference function R′(r, t) provides either the primary or secondary reference. In such cases, it is necessary to consider the constraints of the physical system at hand. For example, in pulse oximetry, it is known that arterial blood, whose signature is the primary plethysmographic wave, has greater oxygen saturation than venous blood, whose signature is the secondary erratic or random signal. Consequently, in pulse oximetry, the ratio of the primary signals due to arterial pulsation r It should also be understood that in practical implementations of the plurality of reference signals and cross correlator technique, the ideal features listed as properties (1), (2) and (3) above will not be precisely satisfied but will be approximations thereof. Therefore, in practical implementations of this embodiment of the present invention, the correlation canceler energy curves depicted in FIG. 7b will not consist of infinitely narrow delta functions but will have finite width associated with them as depicted in FIG. It should also be understood that it is possible to have more than two signal coefficient values which produce maximum energy or power output from a correlation canceler. This situation arises when the measured signals each contain more than two components each of which are related by a ratio as follows: Thus, reference signal techniques together with a correlation cancellation, such as an adaptive noise canceler, can be employed to decompose a signal into two or more signal components each of which is related by a ratio. Once either the secondary reference n′(t) or the primary reference s′(t) is determined by the processor of the present invention, the correlation canceler can be implemented in either hardware or software. The preferred implementation of a correlation canceler is that of an adaptive noise canceler using a joint process estimator. The least mean squares (LMS) implementation of the internal processor The function of the joint process estimator is to remove either the secondary signal portions n The joint process estimator The joint process estimator The joint process estimator The least-squares lattice predictor For each set of samples, i.e. one sample of the reference signal n′(t) or s′(t) derived substantially simultaneously with one sample of the measured signal S The backward prediction error b The same processes are repeated in the least-squares lattice predictor Intermediate variables include a weighted sum of the forward prediction error squares ℑ where λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, i.e., λ≦1. The weighted sum of the backward prediction errors β where, again, λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, i.e., λ≦1. These weighted sum intermediate error signals can be manipulated such that they are more easily solved for, as described in Chapter 9, § 9.3 of the Haykin book referenced above and defined hereinafter in equations (59:1 and (60). The operation of the joint process estimator
After initialization, a simultaneous sample of the measured signal S
if a secondary reference n′(t) is used or according to:
if a primary reference s′(t) is used where, again, λ without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength. Forward reflection coefficient Γ
where a (*) denotes a complex conjugate. These equations cause the error signals f After a good approximation to either the primary signal s In a more numerically stable and preferred embodiment of the above described joint process estimator, a normalized joint process estimator is used. This version of the joint process estimator normalizes several variables of the above-described joint process estimator such that the normalized variables fall between −1 and 1. The derivation of the normalized joint process estimator is motivated in the Haykin text as problem 12 on page 640 by redefining the variables defined according to the following conditions: This transformation allows the conversion of Equations (54)-(64) to the following normalized equations: Initialization of Normalized Joint Process Estimator Let N(t) be defined as the reference noise input at time index n and U(t) be defined as combined signal plus noise input at time index t the following equations apply (see Haykin, p. 619): 1. To initialize the algorithm, at time t=0 set
2. At each instant t≧1, generate the various zeroth-order variables as follows: 3. For regression filtering, initialize the algorithm by setting at time index t=0
4. At each instant t≧1, generate the zeroth-order variable
Accordingly, a normalized joint process estimator can be used for a more stable system. In yet another embodiment, the correlation cancellation is performed with a QRD algorithm as shown diagrammatically in FIG. The following equations adapted from the Haykin book correspond to the QRD-LSL diagram of FIG. 8a (also adapted from the Haykin book). Computations a. Predictions: For time t=1, 2, . . . , and prediction order m=1, 2, . . . , M, where M is the final prediction order, compute: b. Filtering: For order m=0, 1, . . . , M−1; and time t=1, 2, . . . , compute 5. Initialization a. Auxiliary parameter initialization: for order m=1, 2, . . . , M, set
b. Soft constraint initialization: For order m=0, 1, . . . , M, set
ℑ where δ is a small positive constant. c. Data initialization: For t=1, 2, . . . , compute
where μ(t) is the input and d(t) is the desired response at time t. in a signal processor, such as physiological monitor incorporating a reference processor of the present invention to determine a reference n′(t) or s′(t) for input to a correlation canceler, a joint process estimator A flow chart of a subroutine to estimate the primary signal portion s A one-time initialization is performed when the physiological monitor is powered-on, as indicated by an “INITIALIZE NOISE CANCELER” action block Next, a set of simultaneous samples of the composite measured signals S Then, using the set of measured signal samples S A zero-stage order update is performed next as indicated in a “ZERO-STATE UPDATE” action block Next, a loop counter, m, is initialized as indicated in a “m=0” action block Within the loop, the forward and backward reflection coefficient Γ The calculation of regression filter register A new set of samples of the two measured signals S A corresponding flowchart for the QRD algorithm of FIG. 8a is depicted in FIG. 9a, with reference numeral corresponding in number with an ‘a’ extension Physiological monitors may use the approximation of the primary signals s″ A joint process estimator The second regression filter
The second regression filter
The second regression filter has a regression coefficient κ
These values are used in conjunction with those intermediate variable values, signal values, register and register values defined in equations (46) through (64). These signals are calculated in an order defined by placing the additional signals immediately adjacent a similar signal for the wavelength λa. For the constant saturation method, S The addition of the second regression filter An alternative diagram for the joint process estimator of FIG. 10, using the QRD algorithm and having two regression filters is shown in FIG. Once good approximation to the primary signal portions s″
Equations (70) and (71) are equivalent to two equations having three unknowns, namely c
Then, difference signals may be determined which relate the signals of equations (72) through (75), i.e.:
where Δx=x It will be understood that the Δx term drops out from the saturation calculation because of the division. Thus, knowledge of the thickness of the primary constituents is not required to calculate saturation. A specific example of a physiological monitor utilizing a processor of the present invention to determine a secondary reference n′(t) for input to a correlation canceler that removes erratic motion-induced secondary signal portions is a pulse oximeter. Pulse oximetry may also be performed utilizing a processor of the present invention to determine a primary signal reference s′(t) which may be used for display purposes or for input to a correlation canceler to derive information about patient movement and venous blood oxygen saturation. A pulse oximeter typically causes energy to propagate through a medium where blood flows close to the surface for example, an ear lobe, or a digit such as a finger, a forehead or a fetus' scalp. An attenuated signal is measured after propagation through or reflected from the medium. The pulse oximeter estimates the saturation of oxygenated blood. Freshly oxygenated blood is pumped at high pressure from the heart into the arteries for use by the body. The volume of blood in the arteries varies with the heartbeat, giving rise to a variation in absorption of energy at the rate of the heartbeat, or the pulse. Oxygen depleted, or deoxygenated, blood is returned to the heart by the veins along with unused oxygenated blood. The volume of blood in the veins varies with the rate of breathing, which is typically much slower than the heartbeat. Thus, when there is no motion induced variation in the thickness of the veins, venous blood causes a low frequency variation in absorption of energy. When there is motion induced variation in the thickness of the veins, the low frequency variation in absorption is coupled with the erratic variation in absorption due to motion artifact. In absorption measurements using the transmission of energy through a medium, two light emitting diodes (LED's) are positioned on one side of a portion of the body where blood flows close to the surface, such as a finger, and a photodetector is positioned on the opposite side of the finger. Typically, in pulse oximetry measurements, one LED emits a visible wavelength, preferably red, and the other LED emits an infrared wavelength. However, one skilled in the art will realize that other wavelength combinations could be used. The finger comprises skin, tissue, muscle, both arterial blood and venous blood, fat, etc., each of which absorbs light energy differently due to different absorption coefficients, different concentrations, different thicknesses, and changing optical pathlengths. When the patient is not moving, absorption is substantially constant except for the flow of blood. The constant attenuation can be determined and subtracted from the signal via traditional filtering techniques. When the patient moves, this causes perturbation such as changing optical pathlength due to movement of background fluids (e.g., venous blood having a different saturation than the arterial blood). Therefore, the measured signal becomes erratic. Erratic motion induced noise typically cannot be predetermined and/or subtracted from the measured signal via traditional filtering techniques. Thus, determining the oxygen saturation of arterial blood and venous blood becomes more difficult. A schematic of a physiological monitor for pulse oximetry is shown in FIGS. 11-13. FIG. 11 depicts a general hardware block diagram of a pulse oximeter The front end analog signal conditioning circuitry The signal processing system also provides an emitter current control output FIG. 11a illustrates a preferred embodiment for the combination of the emitter drivers The preferred driver depicted in FIG. 11a is advantageous in that the present inventors recognized that much of the noise in the oximeter The voltage reference is also chosen as a low noise DC voltage reference for the digital to analog conversion circuit In the present embodiment, the output of the voltage to current converters In general, the red and infrared light emitters It should be understood that in different embodiments of the present invention, one or more of the outputs may be provided. The digital signal processing system In the present embodiment, the light emitters are driven via the emitter current driver The light signal is attenuated (amplitude modulated) by the pumping of blood through the finger The composite time division signal is provided to the front analog signal conditioning circuitry In the present embodiment, the preamplifier The output of the preamplifier The output of the amplifier The programmable gain amplifier is also advantageous in an alternative embodiment in which the emitter drive current is held constant. In the present embodiment, the emitter drive current is adjusted for each patient in order to obtain the proper dynamic range at the input of the analog to digital conversion circuit The output of the programmable gain amplifier The output of the low-pass filter In one advantageous embodiment, the first analog-to-digital converter The second analog-to-digital converter In addition, by using a single-channel converter, there is no need to tune two or more channels to each other. The delta-sigma converter is also advantageous in that it exhibits noise shaping, for improved noise control. An exemplary analog to digital converter is a Crystal Semiconductor CS5317. In the present embodiment, the second analog to digital converter The digital signal processing system The microcontroller The microcontroller FIGS. 14-20 depict functional block diagrams of the operations of the pulse oximeter In general, the demodulation operation separates the red and infrared signals from the composite signal and removes the 625 Hz carrier frequency, leaving raw data points. The raw data points are provided at 625 Hz intervals to the decimation operation which reduces the samples by an order of 10 to samples at 62.5 Hz. The decimation operation also provides some filtering on the samples. The resulting data is subjected to statistics and to the saturation transform operations in order to calculate a saturation value which is very tolerant to motion artifacts and other noise in the signal. The saturation value is ascertained in the saturation calculation module FIG. 15 illustrates the operation of the demodulation module Because the signal processing system A sum of the last four samples from each packet is then calculated, as represented in the summing operations It should be understood that the 625 Hz carrier frequency has been removed by the demodulation operation FIG. 16 illustrates the operations of the decimation module FIG. 17 illustrates additional functional operation details of the statistics module As represented in FIG. 17, the statistics operation accepts two packets of samples (e.g., 570 samples at 62.5 Hz in the present embodiment) representing the attenuated infrared and red signals, with the carrier frequency removed. The respective packets for infrared and red signals are normalized with a log function, as represented in the Log modules Once the DC signal is removed, the signals are subjected to bandpass filtering, as represented in red and infrared Bandpass Filter modules After filtering, the last 120 samples from each packet (of now 270 samples in the present embodiment) are selected for further processing as represented in Select Last 120 Samples modules Conventional saturation equation calculations are performed on the red and infrared 120-sample packets. In the present embodiment, the conventional saturation calculations are performed in two different ways. For one calculation, the 120-sample packets are processed to obtain their overall RMS value, as represented in the first red and infrared RMS modules In addition to the conventional saturation operation If the cross correlation is too low, the oximeter The red and infrared 120-sample packets are also subjected to a second saturation operation and cross correlation in the same manner as described above, except the 120 samples are divided into 5 equal bins of samples (i.e., 5 bins of 24 samples each). The RMS, ratio, saturation, and cross correlation operations are performed on a bin-by-bin basis. These operations are represented in the Divide Into Five Equal Bins modules FIG. 18 illustrates additional detail regarding the saturation transform module As depicted in FIG. 18, the reference processor It should be understood that the scan values could be chosen to provide higher or lower resolution than 117 scan values. The scan values could also be non-uniformly spaced. As illustrated in FIG. 18, the saturation equation module The ratio “r In other words, assuming that the red and infrared sample packets represent the red S
In the present embodiment, the reference signal vectors and the infrared signal are provided as input to the DC removal module The bandpass filter It should be understood that the red and infrared sample packets may be switched in their use in the reference processor The outputs of the reference processor The joint process estimator also receives a lambda input The joint process estimator The joint process estimator The Master Power Curve module A corresponding transform is completed by the Bin Power Curves module In general, in accordance with the signal model of the present invention, there will be two peaks in the power curves, as depicted in FIG. In order to obtain arterial oxygen saturation, the peak in the power curves corresponding to the highest saturation value could be selected. However, to improve confidence in the value, further processing is completed. FIG. 19 illustrates the operation of the saturation calculation module The saturation calculation module 0.014964670230367 0.098294046682706 0.204468276324813 2.717182664241813 5.704485606695227 0.000000000000000 −5.704482606696227 −2.717182664241813 −0.204468276324813 −0.098294046682706 −0.014964670230367 This filter performs the differentiation and smoothing. Next, each point in the original power curve in question is evaluated and determined to be a possible peak if the following conditions are met: (1) the point is at least 2% of the maximum value in the power curve; (2) the value of the first derivative changes from greater than zero to less than or equal to zero. For each point that is found to be a possible peak, the neighboring points are examined and the largest of the three points is considered to be the true peak. The peak width for these selected peaks is also calculated. The peak width of a power curve in question is computed by summing all the points in the power curve and subtracting the product of the minimum value in the power curve and the number of points in the power curve. In the present embodiment, the peak width calculation is applied to each of the bin power curves. The maximum value is selected as the peak width. In addition, the infrared RMS value from the entire snapshot, the red RMS value, the seed saturation value for each bin, and the cross correlation between the red and infrared signals from the statistics module 404 are also placed in the data bin. The attributes are then used to determine whether the data bin consists of acceptable data, as represented in a Bin Qualifying Logic module If the correlation between the red and infrared signals is too low, the bin is discarded. If the saturation value of the selected peak for a given bin is lower than the seed saturation for the same bin, the peak is replaced with the seed saturation value. If either red or infrared RMS value is below a very small threshold, the bins are all discarded, and no saturation value is provided, because the measured signals are considered to be too small to obtain meaningful data. If no bins contain acceptable data, the exception handling module If some bins qualify, those bins that qualify as having acceptable data are selected, and those that do not qualify are replaced with the average of the bins that are accepted. Each bin is given a time stamp in order to maintain the time sequence. A voter operation The clip and smooth operation In the presently preferred embodiment, the clip and smooth filter During high confidence (no motion), the smoothing filter is a simple one-pole or exponential smoothing filter which is computed as follows:
where x(n) is the clipped new saturation value, and y(n) is the filtered saturation value. During motion condition, a three-pole IIR (infinite impulse response) filter is used. Its characteristics are controlled by three time constants t a a a a b b b FIGS. 20 and 21 illustrate the pulse rate module As further depicted in FIG. 20, the heart rate module The average peak width value provides an input to a motion status module In the case of motion, motion artifacts are suppressed using the motion artifact suppression module In the case of no motion, one of the signals (the infrared signal in the present embodiment) is subjected to DC removal and bandpass filtering as represented in the DC removal and bandpass filter module In the present embodiment, the spectral estimation comprises a Chirp Z transform that provides a frequency spectrum of heart rate information. The Chirp Z transform is used rather than a conventional Fourier Transform because a frequency range for the desired output can be designated in a Chirp Z transform. Accordingly, in the present embodiment, a frequency spectrum of the heart rate is provided between 30 and 250 beats/minute. In the present embodiment, the frequency spectrum is provided to a spectrum analysis module In the case of motion, a motion artifact suppression is completed on the snapshot with the motion artifact suppression module The motion artifact reference processor The motion artifact correlation canceler Because only one saturation value is provided to the reference processor, only one output vector of 270 samples results at the output of the motion artifact suppression correlation canceler As described above, an alternative joint process estimator uses the QRD least squares lattice approach (FIGS. 8a, FIG. 21a depicts an alternative embodiment of the motion artifact suppression module with a joint process estimator The initialization parameters are referenced in FIG. 21a as “Number of Cells,” “Lambda,” “MinSumErr,” “GamsInit,” and “SumErrInit.” Number of Cells and Lambda correspond to like parameters in the joint process estimator Number of Cells=6 Lambda=0.8 MinSumErr=10 GamsInit=10 SumErrInit=10 The clean waveform output from the motion artifact suppression module The output of the spectrum analysis module The output filter Alternative To Saturation Transform Module—Bank Of Filters An alternative to the saturation transform of the saturation transform module There are N filter elements in each filter bank. Each of the filter elements in the first filter bank It should be understood that the number of filter elements can range from 1 to infinity. However, in the present embodiment, there are approximately 120 separate filter elements with center frequencies spread evenly across a frequency range of 25 beats/minute-250 beats/minute. The outputs of the filters contain information about the primary and secondary signals for the first and second measured signals (red and infrared in the present example) at the specified frequencies. The outputs for each pair of matching filters (one in the first filter bank The ratio module The output of the saturation equation modules The results of the histogram provide a power curve similar to the power curve of FIG. It should be understood that as an alternative to the histogram, the output saturation (not necessarily a peak in the histogram) corresponding to the highest saturation value could be selected as the arterial saturation with the corresponding ratio representing r _{a }AND r_{v } As explained above, in accordance with the present invention, primary and secondary signal portions, particularly for pulse oximetry, can be modeled as follows:
Substituting Equation (91) into Equation (89) provides the following:
Note that S As explained above, determining r where i represents time. It should be understood that other correlation functions such as a normalized correlation could also be used. Minimizing this quantity often provides a unique pair of r inverting the two-by-two matrix provides: Thus, Preferably, the correlation of equation (93) is enhanced with a user specified window function as follows: The Blackman Window is the presently preferred embodiment. It should be understood that there are many additional functions which minimize the correlation between signal and noise. The function above is simply one. Thus, In order to implement the minimization on a plurality of discrete data points, the sum of the squares of the red sample points, the sum of the squares of the infrared sample points, and the sum of the product of the red times the infrared sample points are first calculated (including the window function, w These values are used in the correlation equation (93b) Thus, the correlation equation becomes an equation in terms of two variables, r Once r In a further implementation to obtain r where R The correlation between s As explained above, the constraint is that s
In other words, the goal is to maximize equation (94) under the constraint of equation (98). In order to obtain the goal, a cost function is defined (e.g., a Lagrangian optimization in the present embodiment) as follows: where Along the same lines, if we assume that the red and infrared signals S
Because equations (100) and (101) are non-linear in r
These equation (102) and (103) can be solved for x and y. Then, solving for r Solving equation (104) results in two values for r Alternative To Saturation Transform—Complex FFT The blood oxygen saturation, pulse rate and a clean plethysmographic waveform of a patient can also be obtained using the signal model of the present invention using a complex FFT, as explained further with reference to FIGS. 25A-25C. In general, by utilizing the signal model of equations (89)-(92) with two measured signals, each with a first portion and a second portion, where the first portion represents a desired portion of the signal and the second portion represents the undesired portion of the signal, and where the measured signals can be correlated with coefficients r FIG. 25A corresponds generally to FIG. 14, with the fast saturation transform replacing the previously described saturation transform. In other words, the operations of FIG. 25A can replace the operations of FIG. In this alternative embodiment, the snapshot for red and infrared signals is 562 samples from the decimation module The high-pass filter modules The window function modules The complex FFT modules In the first path of processing, the output from the select modules The threshold modules After thresholding, the data points are forwarded to a point-by-point ratio module The phase difference module 6. the red sample must pass the red threshold 7. the infrared sample must pass the infrared threshold 8. the phase between the two points must be less than the predefined threshold as determined in the phase threshold For those sample points which qualify, a ratio is taken in the ratio module The resulting ratios are provided to a saturation equation module which is the same as the saturation equation modules The arterial (and the venous) saturation can then be selected, as represented in the select arterial saturation module The fast saturation transform information can also be used to provide the pulse rate and the clean plethysmographic wave form as further illustrated in FIG. As depicted in FIG. 25C, the input to the window function module The window function module performs a windowing function selected to pass those frequencies that significantly correlate to the frequencies which exhibited saturation values very close to the arterial saturation value. In the present embodiment, the following windowing function is selected: where SAT In order to obtain pulse rate, the output points from the window function module In order to obtain a clean plethysmographic waveform, the output of the windowing function Accordingly, by using a complex FFT and windowing functions, the noise can be suppressed from the plethysmographic waveform in order to obtain the arterial saturation, the pulse rate, and a clean plethysmographic waveform. It should be understood that although the above description relates to operations primarily in the frequency domain, operations that obtain similar results could also be accomplished in the time domain. Relation to Generalized Equations The measurements described for pulse oximetry above are now related back to the more generalized discussion above. The signals (logarithm converted) transmitted through the finger The variables above are best understood as correlated to FIG. 6c as follows: assume the layer in FIG. 6c containing A The wavelengths chosen are typically one in the visible red range, i.e., λa, and one in the infrared range, i.e., λb. Typical wavelength values chosen are λa=60 nm and λb=910 nm. In accordance with the constant saturation method, it is assumed that c In pulse oximetry, it is typically the case that both equations (108) and (109) can be satisfied simultaneously. Multiplying equation (106) by r Multiplying equation (106) by r The constant saturation assumption does not cause the venous contribution to the absorption to be canceled along with the primary signal portions s To illustrate the operation of the oximeter of FIG. 11 to obtain clean waveform, FIGS. 26 and 27 depict signals measured for input to a reference processor of the present invention which employs the constant saturation method, i.e., the signals S FIG. 28 shows the secondary reference signal n′(t)=n It should also be understood that a reference processor could be utilized in order to obtain the primary reference signal s′(t)=s FIGS. 29 and 30 show the approximations s″ It should be understood that approximation n″ Implementing the various embodiments of the correlation canceler described above in software is relatively straightforward given the equations set forth above, and the detailed description above. However, a copy of a computer program subroutine, written in the C programming language, which calculates a primary reference s′(t) using the constant saturation method and, using a joint process estimator The correspondence of the program variables to the variables defined in equations (54)-(64) in the discussion of the joint process estimator is as follows: Δ Γ Γ f b ℑm(t)=nc[m].Fswsqr β γ ρ ρ e e κ κ A first portion of the program performs the initialization of the registers A third portion of the subroutine calculates the primary reference or secondary reference, as in the “CALCULATE PRIMARY OF SECONDARY REFERENCE (s′(t) or n′(t)) FOR TWO MEASURED SIGNAL SAMPLES” action block A fourth portion of the program performs Z-stage update as in the “ZERO STAGE UPDATE” action block A fifth portion of the program is an iterative loop wherein the loop counter, M, is reset to zero with a maximum of m=NC_CELLS, as in the “m=0” action block A sixth portion of the program calculates the forward and backward reflection coefficient Γ A seventh portion of the program, still within the loop begun in the fifth portion of the program, calculates the regression coefficients register The loop iterates until the test for convergence is passed. The test for convergence of the joint process estimator is performed each time the loop iterates analogously to the “DONE” action block The output of the present subroutine is a good approximation to the primary signals s″ It should be understood that the subroutine of Appendix B is merely one embodiment which implements the equations (54)-(64). Although implementation of the normalized and QRD-LSL equations is also straightforward, a subroutine for the normalized equations is attached as Appendix C, and a subroutine for the QRD-LSL algorithm is attached as Appendix D. While one embodiment of a physiological monitor incorporating a processor of the present invention for determining a reference signal for use in a correlation canceler, such as an adaptive noise canceler, to remove or derive primary and secondary components from a physiological measurement has been described in the form of a pulse oximeter, it will be obvious to one skilled in the art that other types of physiological monitors may also employ the above described techniques. Furthermore, the signal processing techniques described in the present invention may be used to compute the arterial and venous blood oxygen saturations of a physiological system on a continuous or nearly continuous time basis. These calculations may be performed, regardless of whether or not the physiological system undergoes voluntary motion. Furthermore, it will be understood that transformations of measured signals other than logarithmic conversion and determination of a proportionality factor which allows removal or derivation of the primary or secondary signal portions for determination of a reference signal are possible. Additionally, although the proportionality factor r has been described herein as a ratio of a portion of a first signal to a portion of a second signal, a similar proportionality constant determined as a ratio of a portion of a second signal to a portion of a first signal could equally well be utilized in the processor of the present invention. In the latter case, a secondary reference signal would generally resemble n′(t)=n Furthermore, it will be understood that correlation cancellation techniques other than joint process estimation may be used together with the reference signals of the present invention. These may include but are not limited to least mean square algorithms, wavelet transforms, spectral estimation techniques, neural networks, Weiner and Kalman filters among others. One skilled in the art will realize that many different types of physiological monitors may employ the teachings of the present invention. Other types of physiological monitors include, but are in not limited to, electro cardiographs, blood pressure monitors, blood constituent monitors (other than oxygen saturation) monitors, capnographs, heart rate monitors, respiration monitors, or depth of anesthesia monitors. Additionally, monitors which measure the pressure and quantity of a substance within the body such as a breathalizer, a drug monitor, a cholesterol monitor, a glucose monitor, a carbon dioxide monitor, a glucose monitor, or a carbon monoxide monitor may also employ the above described techniques. Furthermore, one skilled in the art will realize that the above described techniques of primary or secondary signal removal or derivation from a composite signal including both primary and secondary components can also be performed on electrocardiography (ECG) signals which are derived from positions on the body which are close and highly correlated to each other. It should be understood that a tripolar Laplacian electrode sensor such as that depicted in FIG. 31 which is a modification of a bipolar Laplacian electrode sensor discussed in the article “Body Surface Laplacian ECG Mapping” by Bin He and Richard J. Cohen contained in the journal IEEE Transactions on Biomedical Engineering, Vol. 39, No. 11, November 1992 could be used as an ECG sensor. It must also be understood that there are a myriad of possible ECG sensor geometry's that may be used to satisfy the requirements of the present invention. The same type of sensor could also be used for EEG and EMG measurements. Furthermore, one skilled in the art will realize that the above described techniques can also be performed on signals made up of reflected energy, rather than transmitted energy. One skilled in the art will also realize that a primary or secondary portion of a measured signal of any type of energy, including but not limited to sound energy, X-ray energy, gamma ray energy, or light energy can be estimated by the techniques described above. Thus, one skilled in the art will realize that the techniques of the present invention can be applied in such monitors as those using ultrasound where a signal is transmitted through a portion of the body and reflected back from within the body back through this portion of the body. Additionally, monitors such as echo cardiographs may also utilize the techniques of the present invention since they too rely on transmission and reflection. While the present invention has been described in terms of a physiological monitor, one skilled in the art will realize that the signal processing techniques of the present invention can be applied in many areas, including but not limited to the processing of a physiological signal. The present invention may be applied in any situation where a signal processor comprising a detector receives a first signal which includes a first primary signal portion and a first secondary signal portion and a second signal which includes a second primary signal portion and a second secondary signal portion. Thus, the signal processor of the present invention is readily applicable to numerous signal processing areas. Patent Citations
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