Abstract:
A system and method for signal processing to remove unwanted noise components including: (i) wavelength-independent motion artifacts such as tissue, bone and skin effects, and (ii) wavelength-dependent motion artifact/noise components such as venous blood pulsation and movement due to various sources including muscle pump, respiratory pump and physical perturbation. Disclosed are methods, analytics, and their uses for reliable perfusion monitoring, arterial oxygen saturation monitoring, heart rate monitoring during daily activities and in hospital settings and for extraction of physiological parameters such as respiration information, hemodynamic parameters, venous capacity, and fluid responsiveness. The system and methods disclosed are extendable to include monitoring platforms for perfusion, hypoxia, arrhythmia detection, airway obstruction detection and sleep disorders including apnea.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to U.S. Provisional Application No. 61/926,773 filed Jan. 13, 2014. The above identified patent application is incorporated herein by reference in its entirety to provide continuity of disclosure. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to systems and methods for enhancing physiological signals taken by optical biosensors at different human body sites. In particular, the present invention relates to enhancing photoplethysmographic signals for pulse oximetry, extraction of heart rate, and extraction of other physiological parameters such as respiratory information, fluid responsiveness, perfusion level and other hemodynamic parameters. 
       BACKGROUND 
       [0003]    Photoplethysmography is a non-invasive measurement of the blood flow at the surface of the skin of a human by using two-wavelength lights, such as red (R) and infrared (IR) lights, to generate photoplethysmographic (“PPG”) signals. Two common uses of the PPG signals are calculations of the arterial oxygen saturation and heart rate. Several applications that require various analyses of the PPG signals include amplitude, rhythm, peripheral pulse, respiratory variability and tissue perfusion. For example, increased and decreased signal amplitude can indicate signs of vasodilation and vasoconstriction, respectively. The amplitude is directly proportional to the vascular distensibility. PPG signals are also useful for the detection and diagnosis of cardiac arrhythmias. Further, a PPG signal is known to be sensitive to pulsatile blood flow and captures the peripheral pulses. The pressure at which the pulse is captured highly corresponds to the systolic blood pressure. The respiratory rate can be determined by a set of PPG signals. Noninvasive continuous tissue perfusion and peripheral blood flow detection is another potential advantage of the PPG signal. All the above-mentioned applications require a clean and enhanced signal for feature extraction, analysis, and monitoring. Therefore, the quality of the PPG signal is critical for wearable PPG devices and systems. 
         [0004]    For example, in wearable and implantable devices/applications, biometric signals need to be monitored during daily activities where motion is always present. Motion artifact is the most problematic source of noise which deteriorates signal integrity and can, in the worst case, corrupt the PPG signal to such an extent that the signal is rendered clinically unusable. Examples of motions of the patient in a real world clinical setting include movement during transport, rubbing, waving, seizures, and kicking in neonates and infants. As a result, inaccurate readings and interpretations of the PPG signal due to motion artifact increases the workload of a caregiver of the patient which leads to an increased cost of care and inefficiency of patient&#39;s treatment. Therefore, there is a need in the art for an effective solution for wearable and mobile PPG biosensors to enhance the signal quality in the presence of motion artifact. 
         [0005]    The prior art has attempted to solve these problems with limited success. For example, one commonly used method to reduce the effect of motion artifact is adaptive noise cancellation using accelerometers as a noise reference signal. A two-dimensional active noise cancellation uses the directional accelerometer data for a finger PPG sensor. Another method adds a reflectance PPG sensor as the reference signal to reduce the effect of motion artifact. However, the reflectance PPG sensor is itself susceptible to motion artifact. The main drawback of all these methods is the cost of extra hardware for the generation of the noise reference signal. Further, using accelerometer data is computationally intensive and reflects motion as opposed to motion-induced noise. More precisely, no direct or high correlation between acceleration data from an accelerometer and motion artifact in PPG signal has been found. This method assumes that the original PPG signal has only power at certain frequencies with the remaining power assumed to be noise and then uses Fast Fourier Transform (FFT), Singular Value Decomposition and Independent Component Analysis to generate three synthetic reference noise signals. The method switches between the three reference noise signals by quantifying the randomness of each signal using skewness and kurtosis. These assumptions on motion artifact do not correlate with different real-world sources of noise. Moreover, the highest randomness does not necessarily mean the highest correlation with the true motion artifact in the PPG signal. 
         [0006]    In another example, Masimo Corporation has introduced Discrete Saturation Transform (DST) to find pulse oximeter oxygen saturation in the presence of motion in portable devices. Typically, the DST method includes of a reference signal generator, an adaptive filter and a peak finder to find the most likely SpO 2  value based on the incoming signals. In this approach, the reference signal generator produces reference signals for all possible SpO 2  values. For each reference signal, the adaptive filter produces an output signal. Energy of each output signal is computed and plotted versus corresponding SpO 2  values. The right-most peak of the power plot (the largest saturation value) is nominally considered as oxygen saturation of arterial blood flow. However, this approach does not remove the motion artifact (e.g. due to tissue effect). Consequently, the effect of motion artifact is transformed to the output power plot in DST. More specifically, in presence of motion artifact, new peaks will be present on the output plot and the peak finder fails to find the peak corresponding to accurate SpO 2 . Alternatively, the peak corresponding to SpO 2  is concealed due to high motion noise power causing the peak search to fail for that time window. 
         [0007]    Therefore, there is a need in the art for an effective solution for wearable and mobile PPG biosensors to enhance the signal quality in the presence of motion artifact. 
       SUMMARY 
       [0008]    In a preferred embodiment, a system and method for enhancing PPG signals are disclosed. Different sources of motion-induced error in the PPG signals, which include red and infrared signals are identified, quantified and estimated. Enhanced red and infrared signals are produced by removing these sources of motion induced error. A novel multi-stage adaptive method that efficiently removes the effect of tissue and venous blood noise during motion is disclosed. This method extracts a fundamental period of the PPG signal, the heart rate, and the oxygen saturation level. The method produces a clean enhanced red and infrared PPG signal corresponding to the arterial blood flow. 
         [0009]    In one embodiment, an adaptive and direct capturing of the motion artifact present in circulatory system, including physical motions, respiration and skeletal muscle pumps, and generating enhanced and artifact-free two-wavelength (e.g. R/IR) PPG signals is provided. 
         [0010]    In another embodiment, separation and quantification of arterial and venous pulsations of multi wavelength PPG signals (e.g. R and IR) is provided. 
         [0011]    In another embodiment, identification of biphasic cardiac cycle and sub-heart-beat time intervals where extraction of oxygen saturation and heart rate are minimally impacted by artifact and maximally impacted by the main biometric variation is provided. 
         [0012]    In another embodiment, a method to produce a synthetic noise reference is disclosed. The technique also uses a method for estimating fundamental frequency and noise reference. 
         [0013]    In another embodiment, a first method to enhance red and infrared PPG signals is provided and a method is disclosed to extract the heart rate value. 
         [0014]    In another embodiment, a method to enhance red and infrared PPG signals is provided in combination with a cardiac gating method to extract the oxygen saturation value. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The disclosed embodiments will be described with reference to the accompanying drawings. 
           [0016]      FIG. 1  is a general schematic of a PPG sensor and blood circulation at a measurement site. 
           [0017]      FIG. 2  is a graph of a PPG signal and components of the PPG signal. 
           [0018]      FIG. 3  is a schematic of a system for enhancing PPG signals in a preferred embodiment. 
           [0019]      FIG. 4A  is a flowchart of a model for optimizing a weight of a preferred embodiment. 
           [0020]      FIG. 4B  is a flowchart of a model for finding an optimized weight of a preferred embodiment. 
           [0021]      FIG. 5A  is a flowchart of a method for enhancing a set of PPG signals of a preferred embodiment. 
           [0022]      FIG. 5B  is a block diagram of a system for enhancing a set of PPG signals of a preferred embodiment. 
           [0023]      FIG. 6A  is a block diagram of an adaptive noise canceller with reference noise of a preferred embodiment. 
           [0024]      FIG. 6B  is a block diagram of an adaptive noise canceller with a reference signal of a preferred embodiment. 
           [0025]      FIG. 7  is a block diagram of a real-time fundamental period estimator of a preferred embodiment. 
           [0026]      FIG. 8  is a block diagram of an adaptive noise canceller using synthetic noise reference of a preferred embodiment. 
           [0027]      FIG. 9  is a block diagram of a motion-tolerant signal enhancing and cardiac gating system of a preferred embodiment. 
           [0028]      FIG. 10  is a block diagram of a signal enhancement unit of a preferred embodiment. 
           [0029]      FIG. 11A  is a graph of a sampling window in a biphasic cardiac activity of a preferred embodiment. 
           [0030]      FIG. 11B  is a graph of a sampling window in a biphasic cardiac activity of a preferred embodiment. 
           [0031]      FIG. 11C  is a graph of a sampling window in a biphasic cardiac activity of a preferred embodiment. 
           [0032]      FIG. 11D  is a graph of a sampling window in a biphasic cardiac activity of a preferred embodiment. 
           [0033]      FIG. 12  is a graph of respiratory effect on a baseline of a preferred embodiment. 
           [0034]      FIG. 13  is a block diagram of a cardiac gating unit of a preferred embodiment. 
           [0035]      FIG. 14  is a block diagram of a heart rate extractor of a preferred embodiment. 
           [0036]      FIG. 15  is a block diagram of a correlation canceller of a preferred embodiment. 
           [0037]      FIG. 16  is a schematic of an experimental setup of a preferred embodiment. 
           [0038]      FIG. 17A  is a graph of a raw red PPG signal during various motions of an experiment of a preferred embodiment. 
           [0039]      FIG. 17B  is a graph of a sample PPG signal during an experiment of a preferred embodiment. 
           [0040]      FIG. 17C  is a graph of an autocorrelation of a preferred embodiment. 
           [0041]      FIG. 17D  is a graph of a power spectrum of a preferred embodiment. 
           [0042]      FIG. 17E  is a graph of a heart rate of a preferred embodiment. 
           [0043]      FIG. 17F  is a graph of an SpO 2  of a preferred embodiment. 
           [0044]      FIG. 18A  is a spectrogram of an original PPG signal of a preferred embodiment. 
           [0045]      FIG. 18B  is a spectrogram of an enhanced PPG signal of a preferred embodiment. 
           [0046]      FIG. 19A  is a graph of an ECG waveform from a reference ECG sensor of a preferred embodiment. 
           [0047]      FIG. 19B  a sample PPG signal of a preferred embodiment. 
           [0048]      FIG. 19C  is a graph of heart rates calculated from an original signal and an enhanced signal. 
           [0049]      FIG. 19D  is a graph of a Bland-Altman plot of an original heart rate of a preferred embodiment 
           [0050]      FIG. 19E  is a graph of a Bland-Altman plot of an enhanced heart rate of a preferred embodiment. 
           [0051]      FIG. 19F  is a graph of SpO 2  calculated from an original signal and an enhanced signal. 
           [0052]      FIG. 19G  is a graph of a Bland-Altman plot of SpO 2  calculated from an original signal. 
           [0053]      FIG. 19H  is a graph of a Bland-Altman plot of SpO 2  calculated from an enhanced signal. 
           [0054]      FIG. 20  is a graph of a power plot of the DST method. 
           [0055]      FIG. 21A  is a graph of a Bland-Altman plot of heart rate of a preferred embodiment. 
           [0056]      FIG. 21B  is a graph of a Bland-Altman plot of SpO 2  of a preferred embodiment. 
           [0057]      FIG. 22  is a graph of a simulated portion of a noisy PPG signal. 
           [0058]      FIG. 23A  is a graph of a simulated noisy PPG signal. 
           [0059]      FIG. 23B  is a graph of a fundamental frequency of a preferred embodiment. 
           [0060]      FIG. 23C  is a graph of a portion of an autocorrelation function. 
           [0061]      FIG. 23D  is a graph of an autocorrelation function. 
           [0062]      FIG. 24A  is a graph of an original PPG signal of a preferred embodiment. 
           [0063]      FIG. 24B  is a graph of a heart rate calculated by a fundamental frequency of a preferred embodiment. 
           [0064]      FIG. 24C  is a graph of an autocorrelation function. 
           [0065]      FIG. 25A  is a graph of a motion corrupted PPG signal. 
           [0066]      FIG. 25B  is a graph of an improved PPG signal from an adaptive filter of a preferred embodiment. 
           [0067]      FIG. 25C  is a graph of a synthetic noise reference in time domain of a preferred embodiment. 
           [0068]      FIG. 26A  is a spectrogram of a motion corrupted PPG signal. 
           [0069]      FIG. 26B  is a spectrogram of an improved PPG signal of a preferred embodiment. 
           [0070]      FIG. 26C  is a spectrogram of a synthetic noise reference of a preferred embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0071]    It will be appreciated by those skilled in the art that aspects of the present disclosure may be illustrated and described in any of a number of patentable classes or contexts including any new and useful process or machine or any new and useful improvement. Aspects of the present disclosure may be implemented entirely in hardware, entirely in software (including firmware, resident software, micro-code, etc.) or combining software and hardware implementation that may all generally be referred to herein as a “circuit,” “module,” “unit”, “block”, “method”, “model”, “component,” or “system.” Further, aspects of the present disclosure may take the form of a computer program product embodied in one or more computer readable media having computer readable program code embodied thereon. 
         [0072]    Any combination of one or more computer readable media may be utilized. The computer readable media may be a computer readable signal medium or a computer readable storage medium. For example, a computer readable storage medium may be, but not limited to, an electronic, magnetic, optical, electromagnetic, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of the computer readable storage medium would include, but are not limited to: a hard disk, a random access memory (“RAM”), a read-only memory (“ROM”), an erasable programmable read-only memory (“EPROM” or Flash memory), an appropriate optical fiber with a repeater, a portable compact disc read-only memory (“CD-ROM”), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. Thus, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
         [0073]    A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. The propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of them. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
         [0074]    Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C++, C#, .NET, Objective C, Ruby, Python SQL, MATLAB, or other modern and commercially available programming languages. 
         [0075]    One of the main applications of PPG biosensors is measuring blood oxygen saturation. The commercial device built based upon this technology is a pulse oximeter that uses two or more wave-length lights, such as red and infrared lights. Pulse oximetry may be used to quantify various blood flow characteristics including arterial oxygen saturation, the volume of blood pulsation carried to the tissues, and the heart rate. 
         [0076]    Referring to  FIG. 1 , a pulse oximeter typically uses a set of light emitting diodes (LEDs)  101  with wavelengths in red and infrared regions which emit light at measurement site  100  on a human body. Photodetector  102  captures the transmitted or reflected light. The analog front-end hardware uses a time multiplexed approach with three phases: (i) an activated red LED phase, (ii) an activated infrared LED phase, and (iii) a dark phase. A transimpedance amplifier amplifies the current generated in the photodetector due to optical density during active phases and provides a voltage signal. The voltage signal is filtered, amplified, and sampled with an analog-to-digital converter for further processing. 
         [0077]    The basic circulation of blood is conducted by the heart, which pumps blood periodically and rhythmically into a branching system of arteries. At measurement site  100  (e.g. finger, ear, forehead, nasal), tissues  105  and  106  slightly expand during each heart beat as arterial blood  107  enters capillaries  108  via arteries  103  during systole. The pulsations generated periodically by the heart will dampen by the time they reach capillaries  109 , which are in contact with cells of tissues  105  and  106 . Venous blood  109  then returns via veins  104  in an almost steady stream to the heart with another pulsation stimulated in veins  104  by muscular activity and the respiratory pump. Measurement site  100  contracts as venous blood  109  leaves during diastole. As a result, the path length of the light from the set of LEDs  101  will periodically change. Absorption is proportional to the optical path length according to the Lambert law of optical density and the volume change will be reflected in the output of photodetector  102 . An electronic interface captures these changes via photodetector  102  on the measurement site  100  and provides the PPG signal having a set of component signals. 
         [0078]    Referring to  FIG. 2 , PPG signal  201  includes arterial blood component  202 , venous blood component  203 , capillary blood component  204 , and skin, bone and tissue component  205 . 
         [0079]    Referring to  FIG. 3 , system  300  includes PPG sensor  301  connected to evaluation module  302  and computing device  303  connected to evaluation model  302 . PPG sensor  301  includes red LED  304  and infrared LED  305  and a photodetector. Computing device  303  includes processor  306  and memory  307  connected to processor  306 . Signal enhancement and extraction method  308  is saved in memory  307  and is executed by processor  306 . Evaluation module  302  includes a set of filters and computational units such as multipliers, as will be further described below. Evaluation module  302  receives a red signal from red LED  304  and an infrared signal from infrared LED  305 . Evaluation module  302  processes the red signal and the infrared signal according to signal enhancement and extraction method  308 , as will be further described below. 
         [0080]    In one embodiment, computing device  303  is a personal computer. In another embodiment, computing device  303  is a tablet computer. In another embodiment, computing device  303  is a smartphone. Any computing device known in the art may be employed. 
         [0081]    In one embodiment, computing device  303  is a wearable device, including a wrist-worn device or an electronic patch. In this embodiment, processor  306  and memory  307  are embedded. Any wearable computing device known in the art may be employed. 
         [0082]    In a preferred embodiment, sensor  301  is a wearable sensor that uses red and infrared LEDs working at 660 nm and 895 nm, respectively. Any pulse oximetry sensor known in the art may be employed. Other sensors on various locations of the body and reflection or transmission mode sensors may be employed. 
         [0083]    In a preferred embodiment, evaluation module  302  is an analog front end circuit with an onboard processor. Any evaluation module known in the art may be employed or a custom printed circuit board with custom analog front end may be employed for different applications. The evaluation module includes an analog conditioning circuit which limits the bandwidth of the PPG signal to 70 Hz. In one embodiment, a hamming window and a low-pass filter, with cutoff frequency at 8 Hz, are implemented on the evaluation module in order to attenuate any unwanted signals. 
         [0084]    The source of the PPG signal, red or infrared, is the optical density transmitted or reflected. The basis of optical absorption is defined by Lambert-Beer&#39;s law that explains the optical density (A) for both scatterer and nonscatterer as: 
         [0000]    
       
         
           
             
               
                 
                   A 
                   = 
                   
                     
                       log 
                        
                       
                         ( 
                         
                           
                             L 
                             in 
                           
                           
                             L 
                             out 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       E 
                       · 
                       C 
                       · 
                       D 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0000]    where L in  and L out  are incident and transmitted light intensities, respectively, and C and D are the concentration and thickness of the optical absorber, respectively. E is an extinction coefficient which is intrinsic to the absorber and wavelength. The assumption in this formulation is that the object is uniform and nonscattering and so it only provides a rough estimation about scatterers. 
         [0085]    Two basic theories of optical scattering, which gives a more precise prediction of scattering behaviors, are Rayleigh-Mie&#39;s theory and Schuster&#39;s theory. Aoyagi who reported the principle of pulse oximetry in 1974 has adopted the Schuster&#39;s theory and introduced the optical theory behind photoplethysmography. The following relationship describes the optical density changes ΔA as a function of blood vessel thickness changes AΔD b  for a given blood vessel: 
         [0000]      Δ A =[√{square root over ( E   h ( E   h   +F ))} Hb+Z   b   ]ΔD   b    Eq. 2
 
         [0000]    where E h            S E 0 +(1−S)E r , in which E 0  and E r  are the extinction coefficient of oxyhemoglobin and deoxyhemoglobin, respectively. S is oxygen saturation, Hb is hemoglobin concentrations of the blood and F is the scattering coefficient. Z b  is a constant which becomes zero when the optical receiver is wide enough and independent of the working wavelength. Tissue effect is one of the main sources of error in obtained optical density leading to undesired fluctuation in acquired PPG signals. Considering the effect of tissues, Eq. 2 is modified by adding a new term (Z t  ΔD t ) and becomes: 
         [0000]      Δ A =√{square root over ( E   h ( E   h   +F ))} HbΔD   b   +Z   b   ΔD   b   +Z   t   ΔD   t    Eq. 3
 
         [0000]    where Z t  is approximated to be a constant independent of the wavelength and ΔD t  is thickness change of the tissue. Therefore, there is an optical density change (e.g. Z b  ΔD b+ Z t  ΔD t ) which is wavelength-independent. Eq. 3 considers only one blood vessel. Considering the effect of arterial blood vessels and venous blood vessels, there are arterial blood changes and venous blood changes. Therefore, ΔA is expressed as: 
         [0000]      Δ A =√{square root over ( E   h ( E   h   +F ))} Hb   a   ΔD   b +√{square root over ( E   v ( E   v   +F ))} Hb   v   ΔD   v   +ΔA   s    Eq. 4
 
         [0000]    Subscripts a and v refer to arterial blood and venous blood, respectively. ΔD v  and ΔD a  are venous and arterial blood thickness changes, respectively. ΔA s  is independent of wavelength and it captures the accumulated wavelength-independent effect of blood and tissue thickness changes. Hb a  and Hb v  are arterial and venous hemoglobin concentrations, respectively. 
         [0086]    As will be described below, an optical density is formulated to define a reference signal and a reference noise signal for removal of a tissue effect and a venous effect, respectively. The arterial signal is modeled and a cost function is defined to find the optimum noise reference for removal of venous effect over time. 
         [0087]    When the body remains still, ΔD t  is close to zero and the effect of tissue manifests itself as a DC component in the recorded PPG signal. This DC component can be removed in analog front-end or by digital filtering. However, in the presence of motion, this component is no longer constant. Fluctuations caused by body movements, for example during walking, running and treadmill exercise, can be seen in the recorded PPG signal. Such new rhythmic pattern and variation in the PPG signal can lead to an inaccurate and unreliable fundamental period for the PPG signal. To overcome these issues, two wavelengths are employed to cancel out the effects of Z t , and Z b  that are independent of the wavelength. In a preferred embodiment, optical densities that correspond to a two-wavelength PPG biosensor, as defined in Eq. 4, are subtracted (subscript i and j are used for wavelengths and t to represent tissue effect), and define the result by: 
         [0000]      Δ A   ij     —     t =[√{square root over ( E   a     i   ( E   a     i     +F ))}−√{square root over ( E   a     j   ( E   a     j     +F ))}] Hb   a   ΔD   a +[√{square root over ( E   v     i   ( E   v     t   ( E   v   +F ))}−√{square root over ( E   v     j   ( E   v     j     +F ))}] Hb   v   ΔD   v    Eq. 5
 
         [0088]    The term ΔA s  in Eq. 4 is independent of wavelength and the time difference between recording of both wavelengths is negligible compared to typical time for human motions. This term is now effectively removed in Eq. 5. Consequently, the signal portion due to blood pulsation will remain in M ij     —     t  and the effect of tissue during body movement will be canceled out. 
         [0089]    In a preferred embodiment, a reference signal defined by ΔA ij     —     t  is generated and used in an adaptive filter to enhance signal quality for extracting a PPG fundamental period. The PPG fundamental period will, therefore, be reliably extracted after signal enhancement using the generated reference signal. In another embodiment, the wavelength-independent, i.e., the tissue effect, is applied to more than two wavelengths to remove the tissue noise effect. 
         [0090]    Another main source of error and interference is the change of venous blood during motion artifact. The effect of venous blood appears in the calculation of oxygen saturation more noticeably while the effect of tissue hinders extraction of heart rate. Motion artifact due to tissue effect is removed using ΔA ij     —     t  as a reference signal. The removal of motion artifact is equivalent to setting ΔA s  of Eq. 4 equal to zero. Now that ΔA s  is equal to zero, Eq. 4 for the removal effect of venous blood movement is as follows for a two-wavelength PPG biosensor: 
         [0000]    
       
         
           
               
             
               
                 
                   
                     { 
                     
                       
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 A 
                                 i 
                               
                             
                             = 
                             
                               
                                 
                                   
                                     
                                       E 
                                       
                                         a 
                                         i 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           E 
                                           
                                             a 
                                             i 
                                           
                                         
                                         + 
                                         F 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   Hb 
                                   a 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   a 
                                 
                               
                               + 
                               
                                 
                                   
                                     
                                       E 
                                       
                                         v 
                                         i 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           E 
                                           
                                             v 
                                             i 
                                           
                                         
                                         + 
                                         F 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   Hb 
                                   v 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   v 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 A 
                                 j 
                               
                             
                             = 
                             
                               
                                 
                                   
                                     
                                       E 
                                       
                                         a 
                                         j 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           E 
                                           
                                             a 
                                             j 
                                           
                                         
                                         + 
                                         F 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   Hb 
                                   a 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   a 
                                 
                               
                               + 
                               
                                 
                                   
                                     
                                       E 
                                       
                                         v 
                                         j 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           E 
                                           
                                             v 
                                             j 
                                           
                                         
                                         + 
                                         F 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   Hb 
                                   v 
                                 
                                  
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   D 
                                   v 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     6 
                   
                 
               
             
           
         
       
     
         [0091]    Each of the two sources of information, ΔA i  and ΔA j , is a mixture of arterial blood, represented by subscript a, and venous blood, represented by subscript v, at a particular wavelength (i,j). Each first term of optical density in Eq. 6 represents the arterial blood signal and each second term represents the venous blood signal. Weighted subtraction of these two sources is employed to calculate, a reference noise signal, i.e., ΔA ij   —   v =ΔA i −β ΔA j . Eq. 6 becomes 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               A 
                               
                                 ij 
                                  
                                 
                                     
                                 
                                  
                                 _ 
                                  
                                 
                                     
                                 
                                  
                                 v 
                               
                             
                           
                           = 
                           
                             
                               
                                 [ 
                                 
                                   
                                     ( 
                                     
                                       
                                         r 
                                         a 
                                       
                                       - 
                                       β 
                                     
                                     ) 
                                   
                                    
                                   
                                     
                                       
                                         E 
                                         
                                           a 
                                           i 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             E 
                                             
                                               a 
                                               i 
                                             
                                           
                                           + 
                                           F 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 ] 
                               
                                
                               
                                 Hb 
                                 a 
                               
                                
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 D 
                                 a 
                               
                             
                             + 
                           
                         
                       
                     
                     
                       
                         
                           
                             [ 
                             
                               
                                 ( 
                                 
                                   
                                     r 
                                     v 
                                   
                                   - 
                                   β 
                                 
                                 ) 
                               
                                
                               
                                 
                                   
                                     E 
                                     
                                       v 
                                       i 
                                     
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         E 
                                         
                                           v 
                                           i 
                                         
                                       
                                       + 
                                       F 
                                     
                                     ) 
                                   
                                 
                               
                             
                             ] 
                           
                            
                           
                             Hb 
                             v 
                           
                            
                           Δ 
                            
                           
                               
                           
                            
                           
                             D 
                             v 
                           
                         
                       
                     
                     
                       
                         
                           
                             r 
                             a 
                           
                           = 
                           
                             
                               
                                 
                                   E 
                                   
                                     a 
                                     i 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       E 
                                       
                                         a 
                                         i 
                                       
                                     
                                     + 
                                     F 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               / 
                             
                              
                             
                               
                                 
                                   E 
                                   
                                     a 
                                     i 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       E 
                                       
                                         a 
                                         j 
                                       
                                     
                                     + 
                                     F 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             r 
                             v 
                           
                           = 
                           
                             
                               
                                 
                                   E 
                                   
                                     v 
                                     i 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       E 
                                       
                                         v 
                                         i 
                                       
                                     
                                     + 
                                     F 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               / 
                             
                              
                             
                               
                                 
                                   E 
                                   
                                     v 
                                     j 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       E 
                                       
                                         v 
                                         j 
                                       
                                     
                                     + 
                                     F 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
         [0000]    where r a  is the ratio of arterial optical densities which is linearly related to arterial oxygen saturation and r v  is the ratio of venous optical densities. After removal of the tissue effect, the weighted subtraction of optical densities in Eq. 7 is used to separate two signal sources related to artery and venous. Eq. 7 indicates that with proper tuning of the weight β, the reference noise signal defined by ΔA ij     —     v  may contain a venous component signal, i.e. β=r a , an arterial component signal i.e. β=r v , or a combination of these two sources. In other words, β is swept and a reference noise signal is generated for the various values of β. As can be seen in Eq. 7, there is a range of β where the reference noise signal has the venous component signal and a wider range of β where the reference noise signal has the arterial component signal. 
         [0092]    Separation of the venous component signal in Eq. 7 enables use of the venous component signal as the reference noise signal in an adaptive filter to remove the venous noise from Eq. 6, i.e., generate a venous noise reference signal. In order to find β that removes arterial component signal, i.e., the first term of Eq. 7, and keep the venous component signal, a set of criteria is needed to quantify the performance of any given β. The arterial component signal is a periodic signal with a temporal structure. The more pronounced periodic property of the arterial term in Eq. 7 will be exploited by the subsequent adaptive and prediction error filtering to separate these two signals to estimate of arterial component signal. As will be described below, the optimum β(β opt ) is used in estimating the venous noise reference signal and to implement an adaptive filter for removal of venous blood movement noise. 
         [0093]    Referring to  FIG. 4A , model  400  for optimizing β will be described. Model  400  includes weighted subtractor  401 , adaptive enhancer  402 , and predictor filter  403 . Adaptive enhancer  402  removes the second term of ΔA i  in Eq. 6 and keeps the arterial component signal using the output of weighted subtractor  401  as the reference noise signal  404 . Prediction filter  403  is used to predict the arterial component signal using previous values of the arterial component signal and generate prediction error  405 . Each of input signal  406  x i  and input signal  407  x 2  corresponding to the optical densities ΔA i  and ΔA i  in Eq. 6, is a linear combination of arterial and venous signals. Using arterial and venous optical density ratios, r a  and r v , defined in Eq. 7 , input signal  406  x 1  and input signal  407  x 2  are expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             x 
                             1 
                           
                           = 
                           
                             
                               
                                 r 
                                 a 
                               
                                
                               
                                 s 
                                 a 
                               
                             
                             + 
                             
                               
                                 r 
                                 v 
                               
                                
                               
                                 s 
                                 v 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             x 
                             2 
                           
                           = 
                           
                             
                               s 
                               a 
                             
                             + 
                             
                               s 
                               v 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0094]    Weighted subtractor  401  generates a weighted subtraction of input signals  406  and  407  x 1  and x 2  and generates a reference noise signal  404  corresponding to ΔA ij     —     v  in Eq. 7. Adaptive filter  408  uses reference noise signal  404  to filter out the noise, i.e., the second term of Eq. 6, which is the venous component signal, thereby leaving arterial component signal  409  intact. Arterial component signal  409  is a temporally correlated signal. Adaptive enhancer  402  combines arterial component signal  409  with input signal  404  x 1  to generate enhanced arterial component signal  412 . As shown, the temporal structure of an enhanced arterial signal  412  is modeled with adaptive enhancer  411  with the z-transform of B(z) at the output  410  of adaptive enhancer  411 . Adaptive enhancer  411  models enhanced arterial signal  412 , r a ŝ a (n). B(z) in adaptive enhancer  411  estimates enhanced arterial component signal  412  r a ŝ a  for any given β. For the optimum value of β(β opt ) at  413 , 
         [0000]      r a ŝ a ≈√{square root over (E a     i   (E a     i   +F))}HbΔD a    Eq. 9
 
         [0000]    where √{square root over (E a     i   (E a     i   +F))}Hb ΔD a  is the first term of ΔA i , which is a predictable (periodic) signal, and represents the arterial component signal. Therefore, for β opt , the variance of the prediction error  405  will be minimized. In order to find β opt , model  414  of  FIG. 4B  is employed. 
         [0095]    Referring to  FIG. 4B , in model  414  a linear combination of input signals  406  and  407  x 1  and x 2 , i.e. x 1 −βx 2  with β opt , provides an estimate of the reference venous noise signal at  419 , where 
         [0000]    
       
         
           
             
               β 
               opt 
             
             = 
             
               
                 
                   α 
                    
                   
                       
                   
                    
                   
                     r 
                     v 
                   
                 
                 
                   1 
                   - 
                   α 
                 
               
               . 
             
           
         
       
     
         [0096]    Model  414  extracts a scaled estimate  415 , ŝ as , of the arterial component signal in input signal  406  x 1  at  422  and minimizes the variance of the error signal  417  e(n) at the output of linear predictor  416 . Error signal  418 , e, is the difference between a current sample of scaled estimate  415 , ŝ as (n), and the output B(z) of the linear predictor  416 , i.e., error signal  417  e(n). 
         [0097]    In one embodiment, linear predictor  416  is a Finite Impulse Response (FIR) filter. In another embodiment, linear predictor  416  is an Infinite Impulse Response (IIR) filter. 
         [0098]    The relation between error signal  417  and scaled estimate  415  is mathematically expressed as: 
         [0000]        e ( n )=(1 −B ( z ))ŝ as ( n )   Eq. 10
 
         [0099]    Generally, the FIR embodiment of prediction filter  416  of order P can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                      
                     
                       ( 
                       z 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         l 
                         = 
                         0 
                       
                       P 
                     
                      
                     
                       
                         b 
                         l 
                       
                        
                       
                         z 
                         
                           - 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
         [0100]    Optimization of r v  at  421  and coefficient b of B(z) is determined by minimizing the mean square error defined as the cost function: 
         [0000]        J ( r   v   , b )= E[e   2 ]  Eq. 12
 
         [0000]    where b is the vector of coefficient of prediction filter  416 . In order to simplify the computation and use the extracted fundamental period of the signal, a linear predictor is chosen, B (z)=b z −T     a   , where T a  is the fundamental period of the arterial component signal in discrete time and b is the only coefficient of the filter. The cost function, E[e 2 ], is now written as: 
         [0000]        J ( r   v   ,b )= E[ŝ   as   2 ( n )]−2 bE[ŝ   as ( n ) ŝ   as ( n−T   a )]+ b   2   E[ŝ   as   2 ( n−T   a )]  Eq. 13
 
         [0101]    When the gradients of the cost function with respect to r v  and b are zero, the prediction error, error signal  417  e(n), has its minimum value. So, by equating the gradient of the cost function with respect to r v  and b to zero, we obtain a system of equations. Solving this system of equations for r v  and b, results in: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     v 
                   
                   = 
                   
                     
                       
                         
                           
                             - 
                             
                               E 
                                
                               
                                 [ 
                                 
                                   x 
                                   1 
                                   2 
                                 
                                 ] 
                               
                             
                           
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   
                                     s 
                                     ^ 
                                   
                                   asD 
                                 
                                  
                                 
                                   x 
                                   2 
                                 
                               
                               ] 
                             
                           
                         
                         + 
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   x 
                                   1 
                                 
                                  
                                 
                                   x 
                                   2 
                                 
                               
                               ] 
                             
                           
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   
                                     s 
                                     ^ 
                                   
                                   asD 
                                 
                                  
                                 
                                   x 
                                   1 
                                 
                               
                               ] 
                             
                           
                         
                       
                       
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 x 
                                 2 
                                 2 
                               
                               ] 
                             
                           
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   
                                     s 
                                     ^ 
                                   
                                   asD 
                                 
                                  
                                 
                                   x 
                                   1 
                                 
                               
                               ] 
                             
                           
                         
                         - 
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   x 
                                   1 
                                 
                                  
                                 
                                   x 
                                   2 
                                 
                               
                               ] 
                             
                           
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   
                                     s 
                                     ^ 
                                   
                                   asD 
                                 
                                  
                                 
                                   x 
                                   2 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                      
                     
                         
                     
                      
                     and 
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   14 
                 
               
             
             
               
                 
                   b 
                   = 
                   
                     
                       E 
                        
                       
                         [ 
                         
                           
                             
                               
                                 s 
                                 ^ 
                               
                               as 
                             
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                           
                             
                               
                                 s 
                                 ^ 
                               
                               as 
                             
                              
                             
                               ( 
                               
                                 n 
                                 - 
                                 
                                   T 
                                   a 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     / 
                     
                       E 
                        
                       
                         [ 
                         
                           
                             
                               s 
                               ^ 
                             
                             as 
                           
                            
                           
                             ( 
                             
                               n 
                               - 
                               
                                 T 
                                 a 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   15 
                 
               
             
           
         
       
     
         [0000]    For every given b, including b for which 
         [0000]    
       
         
           
             
               
                 
                   ∂ 
                   
                     J 
                      
                     
                       ( 
                       
                         
                           r 
                           
                             v 
                             , 
                           
                         
                          
                         b 
                       
                       ) 
                     
                   
                 
                 
                   ∂ 
                   
                     r 
                     v 
                   
                 
               
               = 
               0 
             
             , 
           
         
       
     
         [0000]    the error curve is a quadratic function of r v  that includes a single minimum on the error curve. After extraction of the scaled estimate  415  Ŝ as  of the arterial component signal in input signal  406  x 1 , the reference noise signal  419  is extracted by removing the scaled estimate  415  ŝ as  of the arterial component signal from input signal  406  x 1 by minimizing the variance of signal e 1 , reference noise signal  419 . By taking gradient of E[e 1   2 ] with respect to a at  420 , we obtain: 
         [0000]    
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       
                         E 
                          
                         
                           [ 
                           
                             x 
                             1 
                             2 
                           
                           ] 
                         
                       
                       - 
                       
                         
                           r 
                           v 
                         
                          
                         
                           E 
                            
                           
                             [ 
                             
                               
                                 x 
                                 1 
                               
                                
                               
                                 x 
                                 2 
                               
                             
                             ] 
                           
                         
                       
                     
                     
                       E 
                        
                       
                         [ 
                         
                           
                             s 
                             ^ 
                           
                           as 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   16 
                 
               
             
           
         
       
     
         [0102]    Signal e 1  is the reference noise signal  419 . As a result, the linear combination  of signals x 1  and x 2  (i.e. x 1 −βx 2 ) with optimum β, 
         [0000]    
       
         
           
             
               
                 β 
                 opt 
               
               = 
               
                 
                   α 
                    
                   
                       
                   
                    
                   
                     r 
                     v 
                   
                 
                 
                   1 
                   - 
                   α 
                 
               
             
             , 
           
         
       
     
         [0000]    provides an estimate of the reference venous noise signal at  419 . 
         [0103]    Referring to  FIG. 5A , method  500  for signal enhancement and extraction of SpO 2  and heart rate will be described. At step  501 , motion noise due to a tissue effect is removed from a red PPG signal and an infrared PPG signal generating an enhanced red PPG signal and an enhanced infrared PPG signal. At step  502 , a fundamental period is extracted using the enhanced red PPG signal. At step  503 , an optimal venous noise reference signal is determined using the enhanced red PPG signal and the enhanced infrared PPG signal. At step  504 , the enhanced red PPG signal and the enhanced infrared PPG signal are further enhanced using a time-variant optimum venous noise reference signal to generate a clean red PPG signal and a clean infrared PPG signal. At step  505 , a heart rate and a SpO 2  is calculated using the clean red PPG signal and the clean infrared PPG signal. 
         [0104]    Referring to  FIG. 5B , a block diagram of system  506  that implements method  500  will now be described. Red signal  507  and infrared signal  508  are subtracted at  509  to generate reference signal  510 . Reference signal  510  corresponds to ΔA ij     —     t in Eq. 5. Reference signal  510  is used in adaptive filters  511  and  512  to remove motion noise due to tissue and to generate enhanced red signal  513  and enhanced infrared signal  514 , respectively. 
         [0105]    Enhanced red signal  514  is connected to extractor  515 . Extractor  515  extracts fundamental period  516  from enhanced red signal  514 . Extractor  515  is further connected to linear predictor  518 . Linear predictor  518  receives fundamental period  516 . 
         [0106]    After removing motion noise due to tissue effect and extracting fundamental period  516  T a , enhanced red signal  514  x 1  and enhanced infrared signal  513  x 2  are defined by ΔA i  and ΔA j  of Eq. 6, respectively. 
         [0107]    Enhanced infrared signal  513  and enhanced red signal  515  are connected to optimizer  517 . Optimizer  517  is connected to linear predictor  518 . Optimizer  517  and linear predictor  518  generate an optimum weight β  519  (β opt ), as previously described in  FIGS. 4A and 4B . Extracted fundamental period  516  is used in linear predictor  518  to generate prediction error  531  e. The optimum weight β  519  (β opt ) is updated using update rules defined by Eq. 14 and Eq. 16 for r v  and α, respectively. This process is done on a frame basis and for each frame a new β opt  is extracted. β opt  provides an optimum reference noise, consequently, a set of clean signals contain only arterial component needed to extract features such as SpO 2 . 
         [0108]    Weighted subtraction of enhanced infrared signal  513  and enhanced red signal  514  with current β opt  is used to form reference noise  513  defined by Eq. 7 for adaptive filters  524  and  525 . Optimum weight β  519  (β opt  ) is combined with enhanced infrared signal  513  at  520  to form combined signal  521 . Combined signal  521  is combined with enhanced red signal  514  at  522  to generate reference noise  523 . Adaptive filter  524  uses reference noise  523  to remove noise from enhanced infrared signal  513  to generate clean infrared signal  526 . Adaptive filter  525  uses reference noise  523  to remove noise from enhanced red signal  514  to generate clean red signal  527 . Dominant and high power motion noise conceals the waveform amplitude of arterial component when no enhancement algorithm is applied. The disclosed embodiment provides clean signals at the output preserving peak-to-peak values of the arterial signal for amplitude analysis. 
         [0109]    Clean infrared signal  526  and clean red signal  527  are received by extractor  528 . Extractor  528  uses clean infrared signal  526  and clean red signal  527  to calculate SpO 2    529  and heart rate  530 . 
         [0110]    In one embodiment, the ratio of ratios method is employed for the measurement of SpO 2 in pulse oximetry. This method extracts the DC and AC parts of the clean red and infrared PPG signals and computes the ratio of ratios, R, as: 
         [0000]    
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         R 
                         ac 
                       
                        
                       
                         / 
                       
                        
                       
                         R 
                         dc 
                       
                     
                     
                       
                         IR 
                         ac 
                       
                        
                       
                         / 
                       
                        
                       
                         IR 
                         dc 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
         [0000]    where R ac  and R dc  denote the magnitudes of the pulsatile and the DC parts, respectively, of the clean red signal. IR ac  and R dc  are the magnitudes of the pulsatile and DC portions of the clean infrared signal, respectively. In one embodiment, SpO 2  is then calculated by employing the following empirical equation: 
         [0000]        SpO   2 %=( K   1   +K   2   R )%   Eq. 18
 
         [0000]    where K 1  and K 2  are constants empirically found and tuned for a particular sensor platform. For example, K 1  is  105  and K 2  is −23. Other values for K 1  and K 2  may be employed. 
         [0111]    In another embodiment, a correlation-canceller based SpO 2  extraction method is employed, as will be further described below. In another embodiment, Eq. 18 and the correlation-canceller based method are alternatively employed on the type of the motion and the level of the venous blood movement. For example, Eq. 18 is employed on various types of physical motion such as those moving hands/legs, sit-stand body moves, bending, walking, running and their corresponding changes in the levels of venous blood movement. For example, the correlation-canceller based method is employed on various types of motions related to skeletal muscle pump and respiratory pump and their corresponding changes in the levels of venous blood movement. The correlation-canceller based method may be employed during lower rate of change of oxygen saturation or transient severe motion. 
         [0112]    In a preferred embodiment, the fundamental period is the heart rate. In one embodiment, the heart rate is calculated using extractor  515 . In another embodiment, any known heart rate extraction method may be employed based on the application and the need once the clean red and infrared signals are obtained. 
         [0113]    In another embodiment, a correlation-based heart rate extractor is employed to calculate the heart rate, as will be further described below. 
         [0114]    Referring to  FIGS. 6A and 6B , each of the adaptive filters  511 ,  512 ,  524 , and  525  will be further described. Each of adaptive filters  524  and  525  will be further described as adaptive filter  600 . Each of adaptive filters  511  and  512  will be further described as adaptive filter  610 . Each of adaptive filters  600  and  610  includes a filtering process that applies a linear filter on a reference input. 
         [0115]    Referring to  FIG. 6A , filter  603  is applied to reference noise  602  I 2 . Reference noise  602  I 2  is linearly correlated with d(i), the noise component in signal  601  I 1 . By subtracting output  604  {circumflex over (d)}(n) of filter  603  from signal  601  s(n)+d(n) at  605 , enhanced signal  609  and error estimation  606  are generated. Adaptive process  607  automatically updates coefficient  608  of filter  603  based on a set of criteria extracted from error estimation  606 . The set of criteria is defined by adaptive process  607 , as will be further described below. 
         [0116]    Referring to  FIG. 6B , filter  613  is applied to reference signal  612  I 2  to generate enhanced signal  614  s(n). Enhanced signal  614  s(n) is subtracted from signal  611  s(n)+d(n) to generate error estimation  616 . Adaptive process  617  automatically updates coefficient  618  of filter  613  based on a set of criteria extracted from error estimation  616 . The set of criteria is defined by the adaptive process  617 , as will be further described below. 
         [0117]    Referring to  FIGS. 6A and 6B , for each of adaptive processes  607  and  617 , the Least-Mean-Square (LMS) process and its variations are employed. In a preferred embodiment, each of adaptive processes  607  and  617  is the NLMS method due to its lower complexity compared with other techniques and immunity to the fluctuation in the signal energy. Other adaptive optimization techniques including recursive least square may be used. 
         [0118]    In a preferred embodiment, each of filters  603  and  613  is a linear filter. In another embodiment, each of filters  603  and  613  is a nonlinear filter. 
         [0119]    Given the desired output signal, input reference I 2  and the current value of the filter coefficient w(n), the update equation for each of adaptive processes  607  and  617  is expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     w 
                      
                     
                       ( 
                       
                         n 
                         + 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       w 
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                     + 
                     
                       
                         
                           2 
                            
                           η 
                         
                         
                           ɛ 
                           + 
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 0 
                               
                               
                                 N 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 I 
                                 2 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   n 
                                   - 
                                   i 
                                 
                                 ) 
                               
                             
                           
                         
                       
                        
                       
                         
                           I 
                           2 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                        
                       
                         e 
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   19 
                 
               
             
           
         
       
     
         [0000]    where N is the length of the adaptive filter and 0&lt;η&lt;1 and ε is a small number, for example 0.0003, to avoid division by zero due to numerical and fixed point computations. Error estimations  606  and  616  are s(n)+d(n)−{circumflex over (d)}(n) and d(n)+s(n)−ŝ(n), respectively. In adaptive filter  600 , the reference input is only correlated with the noise source. Therefore, minimizing error power minimizes the noise power in mean square sense and enhanced signal  609  is obtained at the output. Similarly, in adaptive filter  610 , the reference input is only correlated with the signal source s(n). Therefore, minimizing error power results in an enhanced noise at the primary output  620 , and an enhanced signal output  614  ŝ(n). An input red or infrared signal corrupted by motion noise is the desired input signal in adaptive filter  610 . The reference signal  611  represents the true signal. 
         [0120]    Referring to  FIG. 7 , step  502  will be further described as method  700 . Method  700  assumes that the period stays the same, i.e. the signal is stationary on each frame. At step  702 , an autocorrelation  706  of an enhanced signal  701  is computed. In this step, the autocorrelation function C(t) preserves periodicity information of enhanced signal  701 . When N samples of enhanced signal  701  are available, the autocorrelation is expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           N 
                           - 
                           1 
                         
                       
                        
                       
                         
                           
                             x 
                             1 
                           
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                          
                         
                           
                             x 
                             1 
                           
                            
                           
                             ( 
                             
                               n 
                               + 
                               t 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   20 
                 
               
             
           
         
       
     
         [0000]    for N larger than several times the period T a  of C(t) where x 1 (n) is enhanced signal  701  which corresponds to enhanced red signal  514  of adaptive filter  512  in  FIG. 5B , t is a lag value and n is discrete time. Both n and t are integers representing time indices. The auto correlation sequence has its maximum value at lag zero and integer multiples of its fundamental period, T a . In one embodiment, the autocorrelation function is linearly combined with the previous autocorrelation functions. In a preferred embodiment, the window length of the autocorrelation function is 1500 samples. Any number of samples may be employed. 
         [0121]    At step  704 , a time domain window  705  is calculated. In this step, for each value of T in the limited range of the period, [Tmin, Tmax], the time domain window 
         [0000]      α 1 δ( t−T )+α 2 δ( t− 2 T )+α 3 δ( t− 3 T )   Eq. 21
 
         [0000]    is generated where δ is dirac delta function. α 1 , α 2  and α 3  are empirically obtained as 1, 0.9, 0.8, respectively, to enhance the accuracy of period estimator and prevent gross errors. 
         [0122]    At step  707 , time domain window  705  is multiplied with autocorrelation function 706 in time domain. This step results in a modified autocorrelation function  708  for each window, which is zero for all values oft except T, 2T and 3T. Different time domain windows may be used. History of heart rate may be used in computation of the heart rate. 
         [0123]    At step  709 , a summation is computed for all modified autocorrelations, at a set of values of T. 
         [0124]    At step  710 , the window passing maximum energy through the autocorrelation function is determined, which defines a fundamental period  711  T a.    
         [0125]    In one embodiment, decreasing amplitude of the time window is considered to reduce susceptibility to period doubling. The extracted fundamental period, T a , is used in prediction error filter to find the optimum β. 
         [0126]    Since method  700  determines the window passing maximum energy instead of searching for peaks in the autocorrelation function, this method is particularly well-suited for noisy environments of wearable sensors. 
         [0127]    In one embodiment, the time window, α 1 δ(t−T)+α 2 δ(t−2T)+α 3 δ(t−3T), is used that represents a train of pulses with fundamental frequency f w  which reduces the leakage from motion noise components. In this embodiment, the frequency domain is determined by finding f w  such that maximum correlation exists between spectrum of the time window and the spectrum of PPG signal. Different window types may be designed and optimized for the PPG signal in the presence of motion artifact. 
         [0128]    Referring to  FIG. 8  in another embodiment, a real-time method  800  for adaptive noise cancellation using a generated synthetic noise reference based on the fundamental frequency is shown. A primary input signal  801 , i.e. s(n)+d(n) contains a raw PPG signal corrupted by motion noise. Estimator  802  uses primary input signal  801  to generate an estimated fundamental frequency  803 . In a preferred embodiment, method  700  is used to estimate the fundamental frequency  803 . 
         [0129]    A reference noise signal  805  g(n) is generated by comb filter  804 . In a preferred embodiment, a comb filter with a transfer function (1−z −Ta )/2 is applied to the primary input signal  801  where T a  is the fundamental frequency  803 . Reference noise signal  805 , g(n) is highly correlated with motion artifact. 
         [0130]    Adaptive filter  806  generates an estimate of motion noise  807  d(n) from reference noise signal  805 . The estimate of motion noise  807  is subtracted from primary input signal  801  at  808  to reduce the noise level and generate enhanced signal  809  and error signal  810 . Adaptive process  811  adapts adaptive filter  806  to minimize power in error signal  810  e(n) by self-adjusting coefficient  812  using a Least Mean Squares method to minimize an error cost function, as previously described. 
         [0131]    Referring to  FIG. 9  in another embodiment, motion-tolerant system  900  includes signal enhancement unit  901  and cardiac gating SpO 2  unit  902 . After conditioning the received red and infrared signals by low pass filtering, preprocessed red signal  903  and preprocessed infrared signal  904  enter signal enhancement unit  901  and the quality of preprocessed red signal  903  and preprocessed infrared signal  904  are improved using adaptive filtering approaches to generate enhanced red signal  905  and enhanced infrared signal  906 . Cardiac gating SpO 2  unit  902  calculates SpO 2    907  using enhanced red signal  905  and enhanced infrared signal  906 . 
         [0132]    Referring to  FIG. 10 , signal enhancement unit  901  will be further described as signal enhancement unit  1000 . Linear phase digital filters  1003  and  1004  remove baseline changes from red signal  1001  and infrared signal  1002 , respectively, to generate red baseline signal  1005  and infrared baseline signal  1006 . Red and infrared LEDs may emit light with different intensities and photodetectors may have different sensitivity at red and infrared wavelengths. Further, the physical condition of site of a measurement such as tissue, bone and skin properties and the length of the measurement site are different from patient to patient. Therefore, red baseline signal  1005  and infrared baseline signal  1006  must be normalized. In a preferred embodiment, each of red baseline signal  1005  and infrared baseline signal  1006 , which shows the mean of the signal over time, is used to normalize red baseline signal  1005  and infrared baseline signal  1006  to generate normalized red signal  1009  and normalized infrared signal  1010 . 
         [0133]    The AC component of normalized red and infrared signals  1009  and  1010  becomes independent of intensity of LEDs and photodetector nonlinear effect. Therefore, they can effectively be compared with each other in parameter extraction units such SpO 2  measurement. After the baseline removal and normalization of red and infrared signals, an intermediate reference signal  1012  is generated by reference signal generator  1011  by subtracting normalized red signal  1009  and normalized infrared signal  1010 . 
         [0134]    Intermediate reference signal  1010  is used by each of FIR adaptive filter  1013  and FIR adaptive filter  1014 . Generally, any correlation canceller can be used for FIR adaptive filter  1013  and FIR adaptive filter  1014 . In a preferred embodiment, each of FIR adaptive filter  1013  and FIR adaptive filter  1014  is adaptive noise canceller  610 . The output of each FIR adaptive filter is a filtered signal and an error signal. FIR adaptive filter  1013  outputs filtered red signal  1015  and FIR adaptive filter  1014  outputs filtered infrared signal  1016 . 
         [0135]    Each filtered signal has a harmonic structure, which is used to further enhance the signal quality in the presence of motion artifact. A harmonic enhancement process is used to enhance the harmonic structure of each filtered signal in the presence of motion. In the harmonic enhancement process, adaptive comb filters  1017  and  1018  adapt to filtered red signal  1015  and filtered infrared signal  1016 , respectively, with a single parameter, fundamental period or fundamental frequency of the respective signal. In a preferred embodiment, fundamental period  1019  is generated and used to adapt each of adaptive comb filters  1017  and  1018 , as will be described below. The output of adaptive comb filter  1017  is an enhanced red signal  1020 . The output of adaptive comb filter  1018  is an enhanced infrared signal  1021 . 
         [0136]    Another issue in ambulatory and portable applications is reliable acquisition of the signals. Presence of the motion leads to fluctuation on baseline and amplitude of the signals and there is a need for a way of controlling the analog front end which prevents nonlinear clipping and provides appropriate signal amplitude at the input of enhancement unit  1000 . In order to prevent clipping and use the available dynamic range of amplifier  1025  in the analog front end, a digital gain and intensity controller  1022  is included. 
         [0137]    Each of red baseline signal  1005  and infrared baseline signal  1006  is measured over time and a moving average filter is applied on each signal by digital gain and intensity controller  1022 . An amplitude of each signal after baseline removal is computed. The photo-detector gain  1023  and LED intensity  1024  is adjusted based on the baseline and AC value of infrared baseline signal  1006 . LED intensity  1024  is converted with digital-to-analog converter  1026  for LED drivers  1027 . LED drivers  1027  drive the LEDs for the red and infrared light based on LED intensity  1024 . The received photo-detector signal is amplified based on the photo-detector  1023  and converted with analog-to-digital converter  1028 . 
         [0138]    In order to reduce the accumulated effect of motion artifact, SpO 2  is preferably calculated on a sub-heart beat time duration. As will be further described below, cardiac gating SpO 2  is employed on sub-heart beat cycle time frames and determines the best time duration in each beat cycle based on the physiology of blood circulation. 
         [0139]    Referring to  FIG. 11A , blood circulation  1100  starts by heart pumping blood into arteries. Blood volume  1101  changes rapidly from minimum  1102  to its maximum value called systolic peak  1103  during systole. Peak to peak interval  1108  is the time between systolic peaks  1103  and  1105 . Pulse interval  1107  is the time between minimum  1102  and minimum  1106 . Sampling interval  1104  is the time between minimum  1102  and systolic peak  1103 . 
         [0140]    Referring to  FIGS. 11A ,  11 B,  11 C, and  11 D, in biphasic cardiac activity when the left ventricular is in systole, the blood flow and hydrodynamic pressure  1109  and  1110  is at a maximum, ventricular ejection time is small, and blood flow velocity is higher. The blood pressure and volume then decrease during diastole  1111  with a slower rate. In a preferred embodiment, the arterial oxygen saturation is sampled and computed during systole, i.e., sampling window  1104 , where the heart pushes blood into the arteries. In this time period, the crest time, blood is mainly controlled by heart as a pump forcing blood into arteries. The amplitude of diastolic peak  1112  in which the heart is relaxing, changes dramatically in the presence of motion compared to systolic time period. Sampling window  1104  is determined during systole and results in a motion-free sampling of the PPG signal during each beat cycle. 
         [0141]    In typical methods, a continuous segment of the PPG signal at a single heartbeat or multiple heart beats is used to compute SpO 2 . In the disclosed cardiac gating SpO 2  method, to improve signal quality, a motion-free short segment of signal in each heart beat is chosen from two or more subsequent cardiac cycles to compute SpO 2 . The heart rate of the patient is an important determinant in cardiac gating. Changes in heart rate over time result in change of location of the motion-free sampling window and length of the sampling window. The disclosed cardiac gating method tracks heart rate changes and the motion-free sampling window over time to build two cardiac synchronized cardiac gated red and infrared signals from which SpO 2  is ultimately calculated. 
         [0142]    Another main contributing error in the presence of motion artifact is the venous return effect of venous blood movement. Venous return blood movement is governed by two physiological processes: (i) respiratory pump and (ii) skeletal muscle pump. The effect of respiratory pump adds a low frequency signal to the PPG signal which is in phase with expiration and inspiration. The respiration rate is typically between 8 to 30 breathes per minute and a respiration cycle takes at least two heart beats. This component of the venous return effect on the PPG signal is in low frequency region. The limited effect of the respiratory portion of venous return on the calculation of the SpO 2  is removed by (i) baseline removal filters in enhancement unit  1000 , as previously described (ii) computation of SpO 2  using the first order derivatives of red and infrared signals (as opposed to original red and infrared signals) and cardiac gating, as will be further described below. Low frequency variation of the respiratory portion of venous return changes the baseline of the signals and when the respiration rate is slow, the baseline will be removed or attenuated by baseline filters or subsequent filtering in signal enhancement unit. Any remaining respiratory related venous return effect is removed by taking the first derivative of the red and infrared signals. 
         [0143]    Referring to  FIG. 12 , graph  1200  shows an experimental result where the user performs a deep long breathe at heart rate of 78 beats per minute. Graph  1200  includes plots of PPG signal  1201 , first derivative  1202  of PPG signal  1201 , and zero line  1203 . Graph  1200  shows the transition between expiration and inspiration phases which represents baseline changes due to respiratory-related venous return. 
         [0144]    Referring to  FIG. 13 , cardiac gating method  1300  for determining a crest time duration of a set of PPG signals will be further described. At step  1303 , a first order derivative of enhanced red signal  1301  is taken to generate first derivative red signal  1305 . In this step, first derivative red signal  1305  is negated to generate negated first derivative red signal  1319 . At step  1304 , a first order derivative of enhanced infrared signal  1302  is taken to generate first derivative infrared signal  1306 . 
         [0145]    At step  1307 , a time window is generated using a set of conditions. The set of conditions determine time durations in which first derivative red signal  1305  is less than or equal to zero, and first derivative infrared signal  1306  is greater than or equal to zero. If this set of conditions exists, then the time window value is one. If not, then the time window is zero. In this step, each of the first order derivative infrared signal  1306  and negated first derivative red signal  1319  is multiplied by the time domain window to generate windowed red signal  1309  and windowed infrared signal  1308 . The time domain windowing step determines the desired time duration from the beginning of the systolic phase up to peak systolic point. 
         [0146]    At step  1310 , heart rate  1312  is extracted using windowed infrared signal  1308 . At step  1311 , windowed infrared signal  1308  and windowed red signal  1309  are “cleaned” using heart rate  1312  to remove the other time durations that do not meet the set of conditions. In order to remove unwanted time durations on the windowed signals and clean each signal, an autocorrelation based method derives the average heart rate for each frame of the data, as previously described, to generate clean red signal  1313  and clean infrared signal  1314 . 
         [0147]    At step  1315 , an optimum ratio  1316  of clean red signal  1313  to clean infrared signal  1314  is calculated in the presence of motion artifact using a correlation canceller ratio measurement, as will be further described below. At step  1317 , SpO 2  is calculated using the optimum ratio  1316 . 
         [0148]    Referring to  FIG. 14 , step  1310  will be further described as method  1400 . Due to its higher amplitude compared to a windowed red signal, windowed infrared signal  1401  is segmented at step  1402 . At step  1403 , for each segment of the windowed infrared signal, an autocorrelation function (ACF) is computed in the range of time periods for human heart rate, as previously described. At step  1404 , a peak finder finds the first dominant peak of the autocorrelation function. 
         [0149]    Fundamental frequency doubling is an issue in fundamental frequency (e.g heart rate) extraction techniques. In the heart rate extraction from a motion-corrupted PPG signal, this issue becomes more troublesome in the presence of the motion artifact which changes the shape of the signal in time domain. 
         [0150]    At step  1405 , a frequency checker removes any frequency doubling. Amplitude of the signal in unwanted time durations is less than amplitude of the signal in the peak systolic point. Therefore, a sliding window with the length of three by average of number of samples in each heart beat moves on the signal. Within this window, the time durations whose peak value of the signal is less than a predetermined threshold multiplied by a mean value are removed. In a preferred embodiment, the predetermined threshold is 0.7. On the modified signal at this point, an autocorrelation function is computed and a peak finder finds the peak value of the autocorrelation function. The maximum peak is chosen for the current window to generate a fundamental frequency  1406 , which is the heart rate. 
         [0151]    Referring to  FIG. 15 , step  1315  will be described as correlation canceller  1500 . Correlation canceller  1500  uses clean infrared signal  1501  as a reference signal (y n ) in a correlation canceller loop. The ratio vector  1503  R n  of length N is available at time n. At step  1504 , an estimated infrared signal  1505  {circumflex over (x)} n  is computed by linear combination of R samples of clean infrared signal  1501  y n . At step  1506 , an error estimation signal  1507  is calculated by e(n)=x(n)−{circumflex over (x)} n  using clean red signal  1502  x(n) and estimated infrared signal  1505  {circumflex over (x)} n . At step  1508 , next ratio vector  1509  R n+1  is calculated by minimizing mean square error of error estimation signal 1507 e(n) with respect to ratio vector R n . Steps  1504 ,  1506 , and  1508  are repeated for next sample, n+1. 
         [0152]    After computing the next ratio vector  1509  of length N, the mean value of ratio vector  1509  is computed and multiplied by the length of the ratio vector N at step  1510  to build a current optimum ratio  1511  of red to infrared light intensities. As seen in  FIG. 15 , the adaptive iterative solution is a gradient-decent method which results in the calculation of the final ratio value from which SpO 2  is derived. 
         [0153]    Test 1 
         [0154]    Referring to  FIG. 16 , experimental sensor platform setup  1600  includes a finger probe  1601  with red LED and infrared LED, respectively, connected to analog and sampling unit  1602 , which is connected to computer  1603 . Analog and sampling unit  1602  includes an analog conditioning circuit which limits the bandwidth of the PPG signal to 70 Hz. The PPG signal is acquired with sampling rate of 250 Hz using a battery powered module with an analog front end circuit and with an onboard processor. A hamming window and a low-pass filter, with cutoff frequency at 8 Hz, are implemented on the evaluation module in order to attenuate any unwanted signals. Other sensors on various locations of the body and reflection or transmission mode sensors may be employed. 
         [0155]    For the performance evaluation, each participant wore a commercially available wireless ECG sensor  1603  and SpO 2  sensor  1604 , each of which is connected to computer  1603  via Bluetooth. The experiment was performed on a treadmill to maintain control over speed and durations. To test and validate the disclosed methods, the PPG signal is collected from different subjects performing various motions. Three experiments are designed to observe effect of motion artifact and quantify signal enhancement using objective and subjective tests. 
         [0156]    The motion types in this test are standing still, up-down “vertical” hand movement, and left-right hand motions of the hand with different speed and acceleration, bending of the finger, walking and running at different speeds. Six subjects between ages of 19-50 participated in the experimentation. For the objective test, an experiment was designed to validate the performance of the disclosed method during normal physical activities (standing, walking and running) One participant, male 28 years old, performed a 30 minute exercise test. This exercise test consisted of 5 minutes walking at 1 mph, 5 min walking at 2 mph, 5 minutes walking in 3 mph, 5 minutes running at 4 mph, 5 minutes running in 5 mph and then a 5 minutes cool down. The cool down included 1 minute running at 4 mph, 1 minute walking at 3 mph, 1 minute walking at 2 mph, 1 minute standing at rest. Six participants completed controlled subjective experiment by walking on the treadmill for 1.5 minutes at 2 mph, then running at the speed of 3.5 mph for another 1.5 minutes and finally running for 2 minutes at 5 mph. 
         [0157]    Referring to  FIG. 17A , graph  1700  shows noisy PPG signal  1701  collected to observe effect of motion artifact through various motions at different time periods. At segment  1702  the user is standing in place. At segment  1703 , the user is moving his hand up and down. At segment  1704 , the user is moving his hand left to right. At segment  1705 , the user is bending the finger to which the PPG sensor is attached. At segment  1706 , the user is walking and running. 
         [0158]    Referring to  FIG. 17B , graph  1707  shows plots  1708  and  1709  of the time domain of the original signal and the enhanced signal, respectively. As can be seen, motion artifact has changed the shape and periodicity of plot  1708  of the original signal. Motion artifact is removed in plot  1709  of the enhanced signal. 
         [0159]    Retelling to  FIG. 17C , graph  1707  shows plots  1711  and  1712  of the autocorrelation function of the original signal and the enhanced signal, respectively. Improvement of the autocorrelation function is observed from plot  1711  of the original signal to plot  1712  of the enhanced signal, which enables a reliable heart rate computation. 
         [0160]    Referring to  FIG. 17D , graph  1713  shows plots  1714  and  1715  of the frequency content of the original signal and the enhanced signal, respectively. 
         [0161]    After reducing the effect of motion, heart rate and SpO 2  are computed every 6 sec (e.g. 1500 samples) with no overlap between frames of data for noisy PPG signal  1701 . 
         [0162]    Referring to  FIG. 17E , graph  1716  shows plots  1717  and  1718  of the extracted heart rate from the original signal and the enhanced signal e.g. after removal of tissue effect, respectively. The fundamental period, extracted using method  1400 , is used for computation of the heart rate for the enhanced signal  1718 . As seen, after enhancing the signal, a robust heart rate computation is provided. 
         [0163]    Referring to  FIG. 17F , graph  1719  shows plots  1720  and  1721  of the SpO 2  calculation from the original signal and the enhanced signal, respectively. SpO 2  computation is very sensitive to motion. The SpO 2  values extracted from the original signal in plot  1720  is unreliable while the enhanced signal e.g. after removal of tissue and venous effect in plot  1721  provides robust computation of the SpO 2 . 
         [0164]    Referring to  FIGS. 18A and 18B , spectrogram  1801  of the original signal and spectrogram  1802  of the enhanced signal are respectively shown. Spectrograms  1801  and  1802  show the effect of motion on the PPG signal. Each spectrogram is computed using Short-Time Fourier Transform (“STFT”) with window size of 2048, overlap size of 1024 and 4096 point Fast Fourier Transform (“FFT”). High power noise component which leads to inaccurate and unreliable computation of the heart rate and SpO 2  is seen in spectrogram  1801 . The removal of high power noise components in spectrogram  1802  leads to restoration of the true power of the signal. Harmonic enhancement is observed in spectrogram  1802  which results in enhancement of the autocorrelation function and reliable heart rate computation. 
         [0165]    Referring to  FIGS. 19A and 19B , graphs  1900  and  1902  show ECG signal curve  1901  and PPG signal curve  1903 , respectively, collected using the ECG sensor and the finger clip PPG sensor, respectively, during the experiment. As shown by ECG signal curve  1901  and PPG signal curve  1903 , there is a corresponding peak value for every QRS complex of ECG waveform. 
         [0166]    Referring to  FIG. 19C , graph  1904  depicts reference heart rate  1905 , original heart rate  1907 , and enhanced heart rate  1906 . 
         [0167]    Referring to  FIGS. 19D and 19E , graph  1908  plots original heart rate  1909  and graph  1919  plots enhanced heart rate  1911 . Graphs  1908  and  1910  show the difference between heart rate computed using original and enhanced signals, respectively. 
         [0168]    Referring to  FIG. 19F , graph  1912  includes the computed SpO 2  for reference stationary signal  1913 , original signal  1915 , and enhanced signal  1915 . As can be seen, before applying the disclosed embodiments, in many cases the ratio of ratios fails to compute the SpO 2.    
         [0169]    Bland-Altman difference plots were used to analyze the agreement between results from the disclosed embodiments and reference measurements. Limit of Agreement (LOA) in this analysis is defined as average difference ±1.96 standard deviation of the difference ([μ−1.96σ,μ+1.96 σ]). 95% of all differences lies inside the LOA. Heart rate and SpO 2  values are extracted every 6 second. 300 pairs of heart rate measurement are obtained. 
         [0170]    Referring to  FIGS. 19G and 19H , graphs  1916  and  1918  include the Bland-Altman plot for SpO 2  computed using original signal  1917  and enhanced signal  1919 , respectively. 
         [0171]    A correlation coefficient is defined as the covariance of the variables divided by their standard deviations. Correlation and agreement analyses are compared in Table 1 below. Much higher correlation and agreement are achieved after enhancing the original signal with the disclosed embodiments for SpO 2  and heart rate. The correlation coefficient of SpO 2  measurement after applying the disclosed embodiments was 0.71 with p-value, i.e., the probability of obtaining a correlation as large as the one obtained randomly, less than 0.00001. There is no correlation between SpO 2  computed from the original signal due to high power noise component in the original signal. For the purpose of comparison, the DST method is also implemented using an adaptive filter of order 32 . Reference signals are generated by sweeping SpO 2  with step size of 0.01 from 0% to 100%. SpO 2  is computed by finding the rightmost peak of the power plot and results are summarized in Table 1 below. There is a low correlation between the DST method and the reference SpO 2  measurements. The disclosed embodiments enhance the original signal to provide a more reliable SpO 2  reading with higher correlation. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 COMPARISON OF HEART RATE AND 
               
               
                 SpO 2  ACHIEVED BEFORE AND AFTER ALGORITHM 
               
             
          
           
               
                   
                   
                 Mean 
                 Mean Abs. 
                   
               
               
                 Parameters 
                 Corr. 
                 Bias 
                 Bias 
                 LOA 
               
               
                   
               
             
          
           
               
                 Heart Rate (Orig.) 
                 0.91 
                 −2.3 
                 8.7 
                 [−23.5, 19.0] 
               
               
                 Heart Rate (Enh.) 
                 0.99 
                 0.36 
                 2.1 
                 [−5.3, 6.0] 
               
               
                 SpO 2  (Orig./Eqn. (19)) 
                 0 
                 −1.8 
                 6.9 
                 [−26.5, 23.0] 
               
               
                 SpO 2  (Orig./DST) 
                 0.1 
                 −5.3 
                 25.6 
                 [−54.3, 43.9] 
               
               
                 SpO 2  (Enh.) 
                 0.73 
                 0.15 
                 0.6 
                 [−1.3, 1.6] 
               
               
                   
               
             
          
         
       
     
         [0172]    Referring to  FIG. 20 , graph  2000  shows common errors where the DST method reports a false reading due to motion artifact. To observe the behavior of the output power plot, SpO 2  is intentionally swept in a larger range. The DST method expects multiple peaks in the range of 0% to 100% where the assumption is that the right-most peak corresponds to arterial oxygen saturation. The amplitude of the peak associated with arterial oxygen saturation is typically very small as shown in curve  2002 . These peaks can easily be affected and concealed by motion artifact as shown in curves  2001  and  2002  where there is no peak related to arterial oxygen saturation on curve  2001 . In curves  2003  and  2004 , not only the peaks are affected by motion artifact but also curves  2003  and  2004  are increasing functions of SpO 2  in the range 0% to 100%. To compare the disclosed embodiment versus the DST method more specifically, we computed the correlation coefficient for various levels of motions, i.e. 1 mph, 3 mph, 5 mph. The correlation coefficient for the disclosed embodiments were 0.85, 0.78, 0.64 and 0.52, .09, .03, for the DST method. 
         [0173]    Referring to  FIGS. 21A and 21B , graphs  2101  and  2102  show the Bland-Altman plot show results for heart rate  2103  and SpO 2    2104 , respectively. A total of 300 heart rate measurement pairs and 295 valid SpO 2  readings were computed after enhancement of the red and infrared signals. Results of this experimentation are summarized in Table 2, below. These results for multi-subject experiment overall show a high level of agreement and correlation between reference measurements and the disclosed method. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 EVALUATION ON MULTI-SUBJECT EXPERIMENT 
               
             
          
           
               
                   
                   
                   
                 Mean 
                 Mean Abs. 
                   
               
               
                   
                 Parameters 
                 Corr. 
                 Bias 
                 Bias 
                 LOA 
               
               
                   
                   
               
             
          
           
               
                   
                 Heart Rate 
                 0.98 
                 −0.57 
                 2.7 
                 [−7.0, 5.9] 
               
               
                   
                 SpO 2   
                 0.7 
                 −0.35 
                 0.71 
                 [−1.9, 1.2] 
               
               
                   
                   
               
             
          
         
       
     
         [0174]    In order to observe sensitivity of filtering to rapid changes of heart rate, the beat-to-beat heart rate was extracted after enhancing the noisy signal with the second stage of the disclosed method while using autocorrelation-based fundamental period extractor and update rule for β opt.    
         [0175]    Due to high similarity of Blood Pressure (BP) signal with the PPG signal, a BP signal from the MIT-BIH polysomnographic database, dataset “slp01a” was used to evaluate the beat-to-beat heart rate. This database includes BP and ECG signals. For evaluation purposes, a reference heart rate is derived from the annotated ECG signal in the database. The BP signal is standardized to have zero mean and unity variance. Noise is artificially added to 1 hour of clean BP signal and signals x 1  and x 2  are generated according to Eq. 8 with r a =0.9 and r v =0.6, which are typical optical density ratios in artery and vein, also in Eq. 7. The noise          (0,1) is filtered with a FIR low pass filter with a cutoff frequency of 8 Hz and multiplied by a gain factor to have unity variance in x 1.    
         [0176]    To extract the beat-to-beat heart rate from the BP signal, a threshold-based method is used which finds the maximum point on the signal in each cycle. The BP signal is converted to frames of size 700 samples. For each new frame, the mean value is subtracted from the signal and a clipping level is extracted by computing a fixed percentage of the maximum amplitude of the signal in that frame. The center clipped signal, i.e., the original signal minus the clipping level, is extracted and a peak finder finds the location of the peak value on the center clipped waveform. The results are summarized in Table 3 below. The relative error in Table 3 is used for quantifying beat-to-beat HR and defined as: 
         [0000]    
       
         
           
             
               
                 
                   Error 
                   = 
                   
                     
                       
                         1 
                         N 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           N 
                         
                          
                         
                           
                             [ 
                             
                               
                                 
                                   HR 
                                    
                                   
                                     ( 
                                     j 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   Ref 
                                    
                                   
                                     ( 
                                     j 
                                     ) 
                                   
                                 
                               
                               
                                 Ref 
                                  
                                 
                                   ( 
                                   j 
                                   ) 
                                 
                               
                             
                             ] 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   22 
                 
               
             
           
         
       
     
         [0177]    where N is the total number of beats, HR is the measured heart rate, and Ref is the reference heart rate obtained from the annotated ECG signal in the database. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 BEAT-TO-BEAT HR 
               
             
          
           
               
                   
                   
                   
                 Mean 
                 Mean Abs. 
                   
               
               
                 Parameters 
                 Error 
                 Corr. 
                 Bias 
                 Bias 
                 LOA 
               
               
                   
               
             
          
           
               
                 Orig. Clean BP 
                 0.021 
                 0.99 
                 0 
                 1.12 
                 [−4.28, 4.28] 
               
               
                 Noisy BP Signal 
                 0.49 
                 0.78 
                 0.10 
                 8.22 
                 [−21.12, 21.24] 
               
               
                 Enh. BP Signal 
                 0.024 
                 0.98 
                 0 
                 1.32 
                 [−4.59, 4.59] 
               
               
                   
               
             
          
         
       
     
         [0178]    The simulation using MIT-BIH database shows that beat-to-beat heart rate is reliably extracted using the disclosed method even though there is an estimation error in the fundamental period due to rapid changes of the heart rate. Due to rapid changes in heart rate and high power of added noise, a threshold-based method has poor performance in extracting the heart rate from a noisy BP signal even though threshold is adaptively adjusted to have the best result. There is a high correlation between beat-to-beat heart rate from the enhanced signal and the reference beat-to-beat heart rate. To further reduce the effect of rhythm irregularities on reference noise in special applications, the disclosed method can be tuned appropriately based on features that are supposed to be extracted from the enhanced output signals for that particular application. For example, the size of autocorrelation window can be tuned based on the rate of changes of heart beat or it can be replaced with an available reliable beat-to-beat heart rate extractor. 
         [0179]    Test 2 
         [0180]    To evaluate the disclosed real-time fundamental estimation method of  FIG. 7 , corrupted and noisy PPG signal named a44091c dataset from MIT MIMIC II waveform database is used. The sampling frequency of this database is 125 Hz and total number of simulated samples is 360000, 48 minutes of data gathered from an Intensive Care Unit (ICU) monitor. 
         [0181]    Referring to  FIG. 22 , plot  2201  of graph  2200  shows a small portion (72 sec) of noisy signal of this dataset. This sample of data includes a noise-free segment from approximately t=18 to approximately t=30 and a noisy segment from approximately t=50 to approximately t=72. 
         [0182]    Referring to  FIGS. 23A ,  23 B,  23 C, and  23 D, graph  2301  includes plot  2302  of raw PPG signal. Graph  2303  includes plot  2304  of the extracted fundamental frequency using the disclosed real-time fundamental frequency estimation method. Graphs  2305  and  2307  include plots  2306  and  2308  of the disclosed autocorrelation method. The heart rate is almost stable and the fundamental frequency is about 1 Hz as it can be visually confirmed by plot  2304 . The result of the disclosed fundamental frequency estimation method is shown in plot  2304 . As can be seen, the frequency estimation method has no error providing a robust estimation of the fundamental frequency. 
         [0183]    In the autocorrelation method, the corresponding autocorrelation function is computed and a peak searching is used to find the fundamental frequency between 0.6 Hz and 3.3 Hz. In this experiment, 2000 data samples are used for computation of autocorrelation. As previously discussed, the autocorrelation function does not provide a robust estimation of fundamental frequency. Several of erroneous outputs are marked by “*” on plots  2306  and  2308 . 
         [0184]    A data collection platform is developed using a finger probe with a red LED and an infrared LED working on 660 nm and 895 nm, respectively. An analog conditioning circuit limits bandwidth of the PPG signal to 70 Hz and the PPG signal is acquired with sampling rate of 250 Hz using a module with an analog front end circuit and with an onboard processor. An FIR hamming window and a low-pass filter with a cutoff frequency at 10 Hz attenuates the unwanted signals. 
         [0185]    To validate the embodiments using synthetic noise generation on real data, the PPG signal from a user performing different motions is collected for 12 minutes. Referring to  FIG. 24A , graph  2401  includes plot  2402  of the PPG signal. Plot  2402  includes segment  2403  of clean data without motion (“No Motion”), segment  2404  of vertical movement of the hand (“UP-Down Motion”), segment  2405  of horizontal movement of the hand (“Left-Right Motion”), segment  2406  bending of the finger (“Bending”), and segment  2407  of walking. Movements have different accelerations and variations within each segment. 
         [0186]    Referring to  FIGS. 24B and 24C , graph  2409  includes plot  2410  of the fundamental frequency calculated by the disclosed fundamental frequency estimation method. Graph  2411  includes plot  2412  of the autocorrelation function. 2500 samples of data are used for computation of the autocorrelation function in both autocorrelation and the fundamental frequency estimation method and results are shown. The disclosed method shows superior and robust performance compared to autocorrelation function in which many errors have occurred during bending of the finger and walking from approximately 6 minutes to approximately 12 minutes. 
         [0187]    Referring to  FIGS. 25A ,  25 B, and  25 C, graph  2501  includes plot  2502  of a motion corrupted PPG signal during left-right movement of the hand. Graph  2503  includes plot  2504  of an improved PPG signal, ŝ(n), at the output of adaptive filter during left-right movement of the hand. Graph  2505  includes plot  2506  of a synthetic noise reference in time domain during left-right movement of the hand. 
         [0188]    Referring to  FIGS. 26A ,  26 B, and  26 C, spectrogram  2601  includes spectrum  2602  of a motion corrupted PPG signal. Spectrogram  2603  includes spectrum  2604  of an improved PPG signal. Spectrogram  2605  includes spectrum  2606  of a synthetic noise reference. As shown, motion artifact components are picked up by the comb filter and the adaptive LMS filter significantly improves the signal spectrogram by reducing noise components of the spectrogram. A normalized LMS adaptive filter of order 20 is used in this experiment. 
         [0189]    It will be appreciated by those skilled in the art that the described embodiments disclose significantly more than an abstract idea including technical advancements in the field of data processing and a transformation of data which is directly related to real world objects and situations in that the disclosed embodiments enable a computer to operate more efficiently and improve medical diagnoses and treatments. Specifically, the disclosed embodiments enhance and clean PPG signals by removing signal noise due to motion and venous blood. The clean PPG signals allow for a faster and more accurate calculation of SpO 2  and heart rate. The faster and more accurate calculation of SpO 2  and heart rate enables more accurate and faster diagnoses and treatment of medical ailments. 
         [0190]    It will be appreciated by those skilled in the art that modifications can be made to the embodiments disclosed and remain within the inventive concept. Therefore, this invention is not limited to the specific embodiments disclosed, but is intended to cover changes within the scope and spirit of the claims.