Abstract:
The present invention provides a plethysmographic signal processing method and system that achieves improved S/N ratios leading to improved patient heart rate estimates and improved plethysmographic waveform displays. The plethysmographic signal processing method and system of the present invention may be implemented using analog and/or digital components within a pulse oximeter. In one embodiment, first and second plethysmographic signals S 1 , S 2  associated with first and second wavelengths, respectively (e.g., infrared and red), are received on first and second channels  210, 212 . First and second multipliers  214, 216  multiply the first and second plethysmographic signals S 1 , S 2  by first and second multiplication factors T 1 , T 2 . A summer  218  sums the products from the first and second multipliers  214, 216  to output a composite plethysmographic signal C on an output channel  220 . The composite plethysmographic signal C may then be displayed and/or utilized to make heart rate determinations and the like.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates generally to the non-invasive determination of patient heart rates from plethysmographic signals, and more particularly to achieving improved signal-to-noise ratios in plethysmographic signals used to estimate patient heart rates and the like.  
         BACKGROUND OF THE INVENTION  
         [0002]    In photoplethysmography, light signals corresponding with two or more different center wavelengths are utilized to non-invasively determine various blood analyte concentrations in a patient&#39;s blood and to obtain information regarding the patient&#39;s heart rate and the like. By way of primary example, blood oxygen saturation (SpO 2 ) levels of a patient&#39;s arterial blood are monitored in pulse oximeters by measuring the absorption of oxyhemoglobin (O2Hb) and reduced hemoglobin (RHb) using red and infrared light signals. The measured absorption data allows for the calculation of the relative concentrations of O2Hb and RHb, and therefore SPO 2  levels, since RHb absorbs more light than O2Hb in the red band and O2Hb absorbs more light than RHb in the infrared band, and since the absorption relationship of the two analytes in the red and infrared bands is known.  
           [0003]    To obtain absorption data, pulse oximeters typically comprise a probe that is releaseably attached to a patient tissue site (e.g., finger, ear lobe, nasal septum, foot). The probe directs red and infrared light signals through the patient tissue site. The light signals are provided by one or more light signal sources (e.g., light emitting diodes or laser diodes) which are typically disposed in the probe. A portion of the red and infrared light signals is absorbed in the patient tissue site and the intensity of the transmitted light signals (light exiting the patient tissue site is referred to as transmitted) is detected by a detector that may also be located in the probe. The detector outputs a signal which includes information indicative of the intensities of the transmitted red and infrared light signals. The output signal from the detector may be processed to obtain separate signals associated with the red and infrared transmitted light signals (i.e., separate red and infrared plethysmographic signals or waveforms).  
           [0004]    As will be appreciated, pulse oximeters rely on the time-varying absorption of light in the patient tissue site as it is supplied with pulsating arterial blood. The patient tissue site may contain a number of non-pulsatile light absorbers, including capillary and venous blood, as well as muscle, connective tissue and bone. Consequently, the red and infrared plethysmographic signals typically contain a large non-pulsatile, or DC, component, and a relatively small pulsatile, or AC, component. Patient heart rate can be determined by examining the time period between successive peaks in the small pulsatile AC component of the red or infrared plethysmographic signals. The small pulsatile AC component of the red or infrared plethysmographic signals can also be displayed on the monitor unit for further observation by persons involved in the treatment of the patient.  
           [0005]    As noted, the pulsatile AC component of a pulse oximeter detector output signal is relatively small compared to the non-pulsatile DC component. Consequently, the accuracy of the heart rate determination and the information which can be obtained through visual perception of the plethysmographic signals on a display can be severely impacted by small amounts of noise. Noise may be introduced by factors such as, for example, motion of the patient tissue site, corruption of the transmitted light signals by ambient light, and noise inherent in the electronic and opto-electronic components of the pulse oximeter. Furthermore, in patients having high SpO 2  levels, the infrared plethysmographic signal typically has a better signal-to-noise (SIN) ratio and is preferred for visual display and heart rate determinations. However, in patients with low SpO 2  levels, the red plethysmographic signal typically has a better SIN ratio and is therefore preferred for visual display and heart rate determinations.  
         SUMMARY OF THE INVENTION  
         [0006]    Accordingly, the present invention provides a plethysmographic signal processing method and system that achieves improved S/N ratios leading to improved patient heart rate estimates and improved plethysmographic waveform displays. The plethysmographic signal processing method and system generates a composite plethysmograhic signal from two or more plethysmographic signals (e.g., red and infrared). The composite plethysmographic signal has an improved S/N ratio over the full range of patient SpO 2  levels as compared to any of the separate plethysmographic signals from which it is generated.  
           [0007]    According to one aspect of the present invention, a plethysmographic signal processing method includes the step of receiving at least two plethysmographic signals. Each plethysmographic signal received is associated with a particular wavelength. In this regard, where there are two plethysmographic signals (e.g., in pulse oximetry), a first one of the plethysmographic signals may be associated with infrared wavelengths (e.g., wavelengths from about 800 nm to about 950 nm), and a second one of the plethysmographic signals may be associated with red wavelengths (e.g., wavelengths from about 600 nm to 700 nm). Each plethysmographic signal received is multiplied by an associated scalar multiplication factor. A composite plethysmographic signal comprising a linear combination of the plethysmographic signals is then generated by adding the results of the multiplications. The plethysmographic signals may be analog signals or digital signals. Where the plethysmographic signals are digital signals, the multiplications and additions are performed for each temporally corresponding signal sample value (i.e., each corresponding-in-time sample instance).  
           [0008]    In the plethysmographic signal processing method, the multiplication factors may be specifically chosen to provide an improved S/N ratio for the composite signal that is generated as compared to the S/N ratios of the separate plethysmographic signals that are received over a specified range of patient SpO 2  levels (e.g., from about 40% to about 100%). In this regard, the multiplication factors may be chosen to depend upon a ratio (e.g., an R value) wherein the ratio varies in accordance with the SpO 2  level in arterial blood circulated through a patient tissue site. By way of example, where there are first and second plethysmographic signals associated with an infrared wavelength and a red wavelength, respectively, first and second multiplication factors designated T 1  and T 2  and associated with the first and second plethysmographic signals, respectively, may be specified in accordance with the following equations:  
         T   1     =     1       1   +     R   2                     T   2     =     -     R       1   +     R   2                                   
 
           [0009]    In the above equations, R may be the ratio of a first differential absorption value dA 1  obtained from the first plethysmographic signal and a second differential absorption value dA 2  obtained from the second plethysmographic signal calculated as follows:  
       R   =            A   2              A   1                               
 
           [0010]    Multiplication factors which depend upon the R value as described above may be obtained in a number of manners. For example, prior to multiplying the plethysmographic signals by their associated multiplication factors, the R value may be computed each time it is needed using the latest differential absorption values available (e.g., from another method or system utilized in a pulse oximeter) and the multiplication factors may be then be computed using the updated R value. As may be appreciated, this is fairly computationally intensive since computation of each multiplication factor requires a multiplication, addition, square root and division operation. As an alternative, the multiplication factors may be obtained from a look-up table. The look-up table includes sets of multiplication factors that are cross-referenced with corresponding incremental R values. The look-up table may, for example, include multiplication factors corresponding with incremental R values ranging from 40% to 100%. In this regard, the R values in the look-up table may, for example, be incremented in equal increments, with the increments being between about 0.001 and about 0.1 in size.  
           [0011]    According to another aspect of the present invention, a signal processing method for use in plethysmography includes the step of receiving first and second plethysmographic signals S 1  and S 2 . The first and second plethysmographic signals S 1  and S 2  are associated with first and second wavelengths, respectively (e.g., infrared and red). A complex signal vector S=S 1 +iS 2  is formed by treating the first plethysmographic signal S 1  as the real component of the complex signal vector S and treating the second plethysmographic signal S 2  as the imaginary component of the complex signal vector S. A complex transformation vector T is also formed from first and second scalar multiplication factors T 1  and T 2 . In this regard, the first scalar multiplication factor T 1  is treated as the real component of the complex transformation vector T and the second scalar multiplication factor T 2  is treated as the imaginary component of the complex transformation vector T (i.e. T=T 1 +iT 2 ). The first and second scalar multiplication factors T 1  and T 2  may depend upon an R value comprising the ratio of a differential absorption value dA 2  obtained from the second plethysmographic signal S 2  to a differential absorption value dA 1  obtained from the first plethysmographic signal S 1 . The complex signal vector S is then multiplied by the complex transformation vector T to generate a composite plethysmographic signal C. The composite plethysmographic signal C achieved has an improved signal strength as compared with either of the first and second plethysmographic signals S 1  and S 2 .  
           [0012]    According to a further aspect of the present invention, a plethysmographic signal processing system includes first and second input channels for receiving first and second plethysmographic signals thereon. The first and second plethysmographic signals are associated with first and second wavelengths, respectively (e.g., infrared and red). The system also includes first and second multipliers. The first multiplier is operable to receive the first plethysmographic signal and a first scalar multiplication factor as inputs and output a first product comprising the first plethysmographic signal multiplied by the first scalar multiplication factor. The second multiplier is operable to receive the second plethysmographic signal and a second scalar multiplication factor as inputs and output a second product comprising the second plethysmographic signal multiplied by the second scalar multiplication factor. The system also includes a summer. The summer is operable to receive the first and second products as inputs and add the first and second products to output a composite signal comprising the sum of the first and second products.  
           [0013]    The first and second plethysmographic signals may comprise continuous time signals, in which case the system of the present invention may be implemented for processing the first and second plethysmographic signals in a continuous time fashion. In the regard, the first channel, second channel, first multiplier, second multiplier, and summer may all comprise analog components. The first and second plethysmographic signals may also comprise discretized-in-time (digital) signals, in which case the system of the present invention may be implemented in software executable by a digital processor.  
           [0014]    The first and second scalar multiplication factors may be dependent upon a ratio (e.g., an R value) that varies in accordance with an SpO 2  level in arterial blood circulated through a patient tissue site. In this regard, the ratio may be computed as follows:  
       R   =            A   2              A   1                               
 
           [0015]    where dA 1  and dA 2  comprise differential absorption values associated with the first and second plethysmographic signals, respectively. The first and second scalar multiplication factors, designated T 1  and T 2 , may be specified in accordance with the following equations:  
         T   1     =     1       1   +     R   2                     T   2     =     -     R       1   +     R   2                                   
 
           [0016]    The system may compute the first and second scalar multiplication factors when needed. Alternatively, the system may further include a look-up table that has multiple pairs of pre-computed first and second scalar multiplication factors cross-referenced with corresponding incremental R values. In this regard, the pairs of first and second scalar multiplication factors may correspond with incremental R values in the range of about 40% to about 100%, with the increments being equal and between about 0.001 and about 0.1 in size.  
           [0017]    Where it is desirable to process additional plethysmographic signals (e.g., third and fourth plethysmographic signals associated with third and fourth wavelengths), the system may include additional input channels for receiving the additional plethysmographic signals. Additional multipliers are also included. The additional multipliers are operable to receive the additional plethysmographic signals and additional scalar multiplication factors as respective inputs and output additional products comprising the respective additional plethysmographic signals multiplied by the respective additional scalar multiplication factors. The summer is then operable to receive as inputs thereto not only the first and second products, but also the additional products as well, and compute the sum of all of the products to output the composite plethysmographic signal.  
           [0018]    These and other aspects and advantages of the present invention will be apparent upon review of the following Detailed Description when taken in conjunction with the accompanying figures. 
       
    
    
     DESCRIPTION OF THE DRAWINGS  
       [0019]    For a more complete understanding of the present invention and further advantages thereof, reference is now made to the following Detailed Description, taken in conjunction with the drawings, in which:  
         [0020]    [0020]FIG. 1 is a block diagram illustrating one embodiment of an exemplary pulse oximeter within which the plethysmographic signal processing method and system of the present invention may be implemented;  
         [0021]    [0021]FIG. 2 is a flow chart illustrating the steps of one embodiment of a plethysmographic signal processing method in accordance with the present invention;  
         [0022]    FIGS.  3 A-B are plots of exemplary complex signal vectors and complex transformation vectors formed in the steps of the plethysmographic signal processing method of FIG. 2;  
         [0023]    [0023]FIG. 4 is a block diagram illustrating one embodiment of a plethysmographic signal processing system in accordance with the present invention;  
         [0024]    [0024]FIG. 5 shows an exemplary look-up table having pairs of first and second multiplication factors cross-referenced with corresponding incremental R values; and  
         [0025]    [0025]FIG. 6 is a plot of exemplary infrared plethysmographic and red plethysmographic signals and a composite signal obtained therefrom by a plethysmographic signal processing system in accordance with the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0026]    Referring to FIG. 1, there is shown an exemplary pulse oximeter  10  within which the plethysmographic signal processing method and system of the present invention may be implemented. The pulse oximeter  10  is configured for use in determining one or more blood analyte levels in a patient tissue site  12 . However, the plethysmographic signal processing method and system of the present invention may be implemented in any device wherein plethysmographic signals are utilized to obtain desired information therefrom.  
         [0027]    The pulse oximeter  10  includes two light signal emitters  20   a - b  (e.g., light emitting diodes or laser diodes) for emitting two light signals  22   a - b  centered at different predetermined center wavelengths λ 1 , λ 2  through the patient tissue site  12  and on to a detector  24  (e.g., a photo-sensitive diode). The center wavelengths λ 1 , λ 2  required depend upon the blood analytes to be determined. For example, in order to determine the levels of O2Hb and RHb, λ 1  may be within the infrared region of the electromagnetic spectrum (e.g., about 800-950 nm) and λ 2  may within the red region of the electromagnetic spectrum (e.g., about 600-700 nm). If more blood analyte levels are to be measured, the pulse oximeter  10  may include additional light signal emitters for emitting light signals centered at additional wavelengths.  
         [0028]    The light signal emitters  20   a - b  and detector  24  may be included in a positioning device  26  to facilitate alignment of the light signals  22   a - b  with the detector  24 . For example, the positioning device  26  may be of clip-type or flexible strip configuration adapted for selective attachment to the patient tissue site  12 . The positioning device  26  may be part of a probe cable unit  28  that is connectable with a separate monitor unit  30 .  
         [0029]    The light signal emitters  20   a - b  are activated by a corresponding plurality of analog drive signals  32   a - b  to emit the light signals  22   a - b . The drive signals  32   a - b  are supplied to the light signal emitters  20   a - b  by a corresponding plurality of drive signal sources  34   a - b . The drive signal sources  34   a - b  may be connected with a digital processor  36 , which is driven with a clock signal  38  from a master clock  40 . The digital processor  36  may be programmed to define modulation waveforms, or drive patterns, for each of the light signal emitters  20   a - b . More particularly, the digital processor  36  may provide separate digital trigger signals  42   a - b  to the drive signal sources  34   a - b , which in turn generate the analog drive signals  32   a - b . The drive signal sources  34   a - b , processor  36  and clock  40  may all be housed in the monitor unit  30 .  
         [0030]    Transmitted light signals  44   a - b  (i.e., the portions of light signals  22   a - b  exiting the patient tissue site  12 ) are detected by the detector  24 . The detector  24  detects the intensities of the transmitted signals  44   a - b  and outputs a current signal  46  wherein the current level is indicative of the intensities of the transmitted signals  44   a - b . As may be appreciated, the current signal  46  output by the detector  24  comprises a multiplexed signal in the sense that it is a composite signal including information about the intensity of each of the transmitted signals  44   a - b . Depending upon the nature of the drive signals  32   a - b , the current signal  46  may, for example, be time-division multiplexed, wavelength-division multiplexed, or code-division multiplexed.  
         [0031]    The current signal  46  is directed to an amplifier  48 , which may be housed in the monitor unit  30  as is shown. The amplifier  48  converts the current signal  46  to a voltage signal  50  wherein a voltage level is indicative of the intensities of the transmitted signals  22   a - b . The amplifier  48  may also be configured to filter the current signal  46  from the detector  24  to reduce noise and aliasing. By way of example, the amplifier  48  may include a bandpass filter to attenuate signal components outside of a predetermined frequency range encompassing modulation frequencies of the drive signals  32   a - b.    
         [0032]    Since the current signal  46  output by the detector  24  is a multiplexed signal, the voltage signal  50  is also a multiplexed signal, and thus, the voltage signal  50  must be demultiplexed in order to obtain signal portions corresponding with the intensities of the transmitted light signals  44   a - b . In this regard, the digital processor  36  may be provided with demodulation software for demultiplexing the voltage signal  50 . In order for the digital processor  36  to demodulate the voltage signal  50 , it must first be converted from analog to digital. Conversion of the analog voltage signal  50  is accomplished with an analog-to-digital (A/D) converter  52 , which may also be included in the monitor unit  30 . The A/D converter  52  receives the analog voltage signal  50  from the amplifier  48 , samples the voltage signal  50 , and converts the samples into a series of digital words  54  (e.g., eight, sixteen or thirty-two bit words), wherein each digital word  54  is representative of the level of the voltage signal  50  (and hence the intensities of the transmitted light signals  44   a - b ) at a particular sample instance. In this regard, the A/D converter  52  should provide for sampling of the voltage signal  50  at a rate sufficient to provide for accurate tracking of the shape of the various signal portions comprising the analog voltage signal  50  being converted. For example, the A/D converter  52  may provide for a sampling frequency at least twice the frequency of the highest frequency drive signal  32   a - b , and typically at an even greater sampling rate in order to more accurately represent the analog voltage signal  50 .  
         [0033]    The series of digital words  54  is provided by the A/D converter  52  to the processor  36  to be demultiplexed. More particularly, the processor  36  may periodically send an interrupt signal  56  (e.g., once per every eight, sixteen or thirty-two clock cycles) to the A/D converter  52  that causes the A/D converter  52  to transmit one digital word  54  to the processor  36 . The demodulation software may then demultiplex the series of digital words  54  in accordance with an appropriate method (e.g., time, wavelength, or code) to obtain two digital signal portions indicative of the intensities of each of the transmitted light signals  44   a - b.    
         [0034]    The demultiplexed digital signal portions comprise first and second plethysmographic signals S 1  and S 2  associated with the two separate center wavelengths λ 1 , λ 2  (e.g., infrared and red) of the transmitted light signals  44   a - b . The first and second plethysmographic signals S 1  and S 2  may then be processed to obtain desired information therefrom such as O2Hb and RHb levels in the patient tissue site  12  as well as the patient&#39;s heart rate. In this regard, the first and second plethysmographic signals S 1  and S 2  may be processed in accordance with the steps of the plethysmographic signal processing method of the present invention in order to generate a composite plethysmographic signal C having an improved SIN ratio as compared to either of the first and second plethysmographic signals S 1  and S 2 . The composite plethysmographic signal C may then be displayed on a display device  58  of the monitor unit  30  and processed further to obtain the patient&#39;s heart rate.  
         [0035]    Referring now to FIG. 2 the steps of one embodiment of a plethysmographic signal processing method in accordance with the present invention are shown. The method begins with step  100  wherein first and second plethysmographic signals S 1  and S 2  are received. In this regard, the plethysmographic signals S 1  and S 2  may be received from the detector of a pulse oximeter probe, either directly or after appropriate amplification and filtering. Typically, the plethysmographic signals S 1  and S 2  will be associated with infrared and red wavelength optical signals transmitted by the probe through a patient tissue site, although plethysmographic signals associated with other wavelength optical signals may be processed in accordance with the steps of the plethysmographic signal processing method described herein.  
         [0036]    The infrared and red plethysmographic signals S 1  and S 2  are separately processed to obtain an R value associated therewith. The R value is defined as the ratio of red optical signal absorption in the patient tissue site to infrared optical signal absorption in the patient tissue site and provides information regarding oxygen saturation of hemoglobin in arterial blood circulated through the patient tissue site (higher R values indicate lower oxygen saturation levels). In this regard, the R value may computed as the ratio of a red delta absorption value dA Red  to an infrared delta absorption value dA Infrared  (i.e. R=dA Red /dA Infrared ). The delta absorption values dA Red , dA Infrared  and the R value depending thereon may, for example, be obtained from the infrared and red plethysmographic signals S 1  and S 2  as described in U.S. Pat. No. 5,934,277 entitled “SYSTEM FOR PULSE OXIMETRY SPO2 DETERMINATION”, the disclosure of which is incorporated herein in its entirety.  
         [0037]    In step  110 , a complex signal vector S is formed using the received plethysmographic signals S 1  and S 2 . The complex signal vector S is formed by treating the first plethysmographic signal S 1  as the real component of the complex signal vector S and treating the second plethysmographic signal S 2  as the imaginary component of the complex signal vector S (i.e., S=S 1 +iS 2 ). In this regard, exemplary complex signal vectors S formed from infrared and red plethysmographic signals S 1  and S 2  at a particular instant in time having respective R values of 0.5 (normal oxygen saturation) and 2.0 (low oxygen saturation) are illustrated in FIGS.  3 A-B. In FIGS.  3 A-B, the complex signal vectors S have been normalized to have magnitudes of 1.0 and plotted on a coordinate system where the infrared component of the complex signal vector S corresponds with the real axis and the red component of the complex signal vector S corresponds with the imaginary axis. The slopes of the complex signal vectors S correspond with their respective R values.  
         [0038]    In step  120 , first and second scalar multiplication factors T 1  and T 2  are obtained. The first and second scalar multiplication factors T 1  and T 2  are chosen such that multiplication of the complex signal vector S (see step  140 ) by a complex transformation vector T formed from the multiplication factors (see step  130 ) rotates the complex signal vector S onto the real axis of the coordinate system. In this regard, the first and second scalar multiplication factors T 1  and T 2  depend upon the R value and are given by the following equations:  
         T   1     =     1       1   +     R   2                     T   2     =     -     R       1   +     R   2                                   
 
         [0039]    Where the first and second plethysmographic signals S 1  and S 2  are associated with optical signal wavelengths other than infrared and red, the first and second multiplication factors T 1  and T 2  may be given by different equations and depend upon factors other than the R value.  
         [0040]    The first and second scalar multiplication factors T 1  and T 2  may be obtained in several manners. They may be computed as needed using the most recently updated R value in accordance with above equations for T 1  and T 2 . Alternatively, pairs of first and second scalar multiplication factors T 1  and T 2  corresponding with various incremental R values can be computed in advance in accordance with the above equations for T 1  and T 2  and stored in a lookup table. When needed, the first and second scalar multiplication factors T 1  and T 2  corresponding with the most recently updated R value are selected from the lookup table.  
         [0041]    In step  130 , a complex transformation vector T is formed using the scalar multiplication factors T 1  and T 2  obtained in step  120 . In this regard, the complex transformation vector T is formed by treating the first scalar multiplication factor T 1  as the real component of the complex transformation vector T and treating the second scalar multiplication factor T 2  as the imaginary component of the complex transformation vector T (i.e., T=T 1 +iT 2 ). Exemplary complex transformation vectors T formed using the scalar multiplication factors T 1  and T 2  obtained in accordance with the formulas for T 1  and T 2  described in connection with step  120  using respective R values of 0.5 (normal oxygen saturation) and 2.0 (low oxygen saturation) are illustrated in FIGS.  3 A-B.  
         [0042]    In step  140 , the complex signal vector S is multiplied by the complex transformation vector T to generate a composite plethysmographic signal C. Multiplication of the complex signal vector S by the complex transformation vector T results in rotation of the complex signal vector S onto the real axis of the coordinate system because appropriate scalar multiplication factors T 1  and T 2  have been employed in forming the complex transformation vector T. In this regard, as can be seen for the exemplary complex signal vectors S and complex transformation vectors T illustrated in FIGS.  3 A-B, the complex transformation vectors T are the reflections of the complex signal vectors S across the real axis (i.e., they are the complex conjugates of the complex signal vectors S). Rotation of the complex signal vector S onto the real axis results in a composite plethysmographic signal C which has improved signal strength as compared with either of the first and second plethysmographic signals S 1  and S 2 .  
         [0043]    The following two examples illustrate the improvements in signal strength that are obtained by processing the red and infrared plethysmographic signals in accordance with the method of the present invention.  
       EXAMPLE 1  
       [0044]    In the following example, it is assumed that R=0.5 and that the magnitude of the complex signal vector S is 1.0. Such a situation is representative of a normal (i.e., high SpO 2  saturation) patient. As is illustrated in FIG. 3A, the slope of the complex signal vector S formed by combining the infrared and red signals S 1 , S 2  has a slope of 0.5 and a length of 1.0. The projection of the complex signal vector S onto the infrared axis is 0.894 and the projection of the complex signal vector S onto the red axis is 0.447. Thus, the infrared signal S 1  has a better S/N ratio than the red signal S 2 . The complex signal vector S is rotated into the real axis by multiplying the complex signal vector S by the complex signal transformation vector:  
               T   =       T   1     +     i                   T   2                     =       1       1   +     R   2           -     i        R       1   +     R   2                           =       1       1   +     0.5   2           -     i        0.5       1   +     0.5   2                           =     0.894   -     0.447      i                                         
 
         [0045]    The following result is obtained:  
                 S   *   T     =       (     0.894   +     0.447      i       )          (     0.894   -     0.447      i       )                   =     0.7992   -     0.3996      i     +     0.3996      i     -     0.1998        i   2                     =   1.0                                     
 
         [0046]    The result obtained is nearly an 11% increase in signal strength as compared with using the infrared signal by itself.  
       EXAMPLE 2  
       [0047]    In the following example, it is assumed that R=2.0 and that the magnitude of the complex signal vector S is 1.0. Such a situation is representative of a sick (i.e., low SpO 2  saturation) patient. As is illustrated in FIG. 3B, the slope of the complex signal vector S formed by combining the infrared and red signals S 1 , S 2  has a slope of 2.0 and a length of 1.0. In this example, the projection of the complex signal vector S onto the infrared axis is now 0.447 and the projection of the complex signal vector S onto the red axis is now 0.894. Here, the red signal S 2  has a better S/N ratio than the infrared signal S 1 . The complex signal vector S is rotated into the real axis by multiplying the complex signal vector S by the complex transformation vector:  
               T   =       T   1     +     i                   T   2                     =       1       1   +     R   2           -     i        R       1   +     R   2                           =       1       1   +     2.0   2           -     i        2.0       1   +     2.0   2                           =     0.447   -     0.894      i                                         
 
         [0048]    The following result is obtained:  
                 S   *   T     =       (     0.447   +     0.894      i       )          (     0.447   -     0.894      i       )                   =     0.1998   -     0.3996      i     +     0.3996      i     -     0.7992        i   2                     =   1.0                                     
 
         [0049]    Here, the result obtained is over a 123% increase in signal strength as compared with using the infrared signal by itself.  
         [0050]    Exemplary System For Implementing Plethysmographic Signal Processing Method  
         [0051]    Referring now to FIG. 4, there is shown a block diagram of one embodiment of a system  200  for implementing the plethysmographic signal processing method of the present invention. In configuring the system  200 , it has been recognized that the method of the present invention can be simplified. In this regard, assuming R is correct, it contains only noise and motion and therefore, only the real part of the result obtained when multiplying the complex signal vector S by the complex transformation vector T needs to be computed and the imaginary part of the result can be ignored.  
         [0052]    The system  200  includes an infrared channel  210  for receiving an infrared plethysmographic signal S 1  thereon and a red channel  212  for receiving a red plethysmographic signal S 2  thereon. A first multiplier  214  takes as inputs the infrared signal S 1  received on the infrared channel  210  and a first multiplication factor T 1  and outputs the result of the first multiplication factor T 1  times the infrared signal S 1 . A second multiplier  216  takes as inputs the red signal S 2  received on the red channel  212  and a second multiplication factor T 2  and outputs the result of the second multiplication factor T 2  times the red signal S 2 . The results output by the first and second multipliers  214 ,  216  are directed to a summer  218  which adds the multiplication results together and outputs the composite signal C on an output channel  220  of the system  200 .  
         [0053]    The system  200  may be implemented in analog components, in which case the multiplication and summing operations are performed in continuous time. Alternatively, the system  200  may be implemented using digital technologies (e.g., in software executable by the processor  36  of the monitor unit of a pulse oximeter  10  such as described in connection with FIG. 1), in which case the multiplication and summing operations are performed on discrete time samples.  
         [0054]    The first and second multiplication factors T 1 , T 2  depend upon the R value and are computed in accordance with the previously described formulas. Since the R value typically changes infrequently, the first and second multiplication factors T 1 , T 2  can be computed infrequently (e.g., only when the R value changes) to reduce the computational requirements of the system  200 . Further computational efficiencies can be achieved by computing first and second multiplication factors T 1 , T 2  corresponding with a range of incremental R values in advance and storing the pre-computed multiplication factors T 1 , T 2  in a lookup table  230  accessible to the system  200  (e.g., on an EPROM chip). In this regard, first and second multiplication factors T 1 , T 2  may be pre-computed for R values ranging, for example, from 0.40 to 1.40 in, for example, 0.01 increments (i.e. for R=0.98, 0.99, 1.00, 1.01, 1.02, . . . ). FIG. 5 shows an exemplary look-up table  230  wherein the R values are incremented from 0.0 to 4.0 in equal 0.1 increments. Numerous other R value ranges and increments, equal or unequal, may be utilized depending upon factors such as the amount of precision desired and the amount of memory available for storing the lookup table. When needed, the first and second multiplication factors T 1 , T 2  corresponding with the current R value are read from the lookup table. If there are no entries in the lookup table for the current R value, interpolation techniques may be employed or the current R value may be appropriately rounded to obtain the first and second multiplication factors T 1 , T 2 .  
         [0055]    Plots of exemplary infrared plethysmographic and red plethysmographic signals S 1 , S 2  and a composite signal C obtained using a system  200  such as described above implemented in computer software executable by a digital processor are shown in FIG. 6. In FIG. 6 the DC portions (i.e., the non-pulsatile components) of the signals S 1 , S 2  and C have been normalized (i.e., set equal to 1.0) to emphasize the AC portions (i.e., the small pulsatile components) of the signals S 1 , S 2  and C. As can be seen from FIG. 6, the composite signal C generated by the system  200  has a significantly greater peak-to-peak (i.e., high point to low point) amplitude difference than either the infrared or red plethysmographic signals S 1  and S 2  making it easier to perform heart-rate calculations and the like using the composite signal S and making the composite signal S easier to perceive visually on a display.  
         [0056]    While various embodiments of the present invention have been described in detail, further modifications and adaptations of the invention may occur to those skilled in the art. However, it is to be expressly understood that such modifications and adaptations are within the spirit and scope of the present invention.