Patent Publication Number: US-2013245482-A1

Title: Signal processing techniques for aiding the interpretation of respiration signals

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 12/481,045, filed Jun. 9, 2009, which is incorporated by reference herein in its entirety. 
    
    
     SUMMARY 
     The present disclosure is related to signal processing systems and methods, and more particularly, to systems and methods for processing respiration signals. 
     In an embodiment, a respiration signal may be processed to normalize respiratory feature values of the signal. Respiration signals may indicate the breathing patterns of a patient over time. Respiratory features (e.g., signal peaks) within the respiration signal may reflect the breathing of the patient. Respiratory features within the respiration signal may also reflect noise or other artifacts. The respiration signal may be normalized by reducing variations in the respiratory feature values within the respiration signal. Normalizing the respiration signal may reduce the effect of noise or other artifacts on the respiration signal and may aid in the interpretation and/or analysis of the respiration signal. For example, normalizing the respiration signal may aid in the determination of respiration parameters such as respiration rate. 
     In an embodiment, a respiration signal may be obtained using a sensor capable of measuring the respiration of a patient or by deriving the respiration signal from another suitable biosignal. Respiratory features such as signal peaks (e.g., local maxima and/or minima in the signal amplitude versus time) in the respiration signal may be identified and signal peak thresholds may be determined. In an embodiment, signal peak threshold values may be determined based on the values of the identified signal peaks. For example, signal peak threshold values may be related to a mean value, a weighted mean value, a median value, a value at a certain percentile of distribution of values, or any other suitable value. An upper signal peak threshold value may be used to identify signal peaks having values that exceed a particular value. A lower signal peak threshold value may be used to identify signal peaks having values that are below a particular value. The identified signal peaks may then be adjusted based on the determined signal peak threshold values to normalize the respiration signal. 
     In an embodiment, a portion of the respiration signal surrounding an identified signal peak may be selected and the entire selected portion of the signal may be adjusted. For example, a signal segment may be a portion of the signal that begins at a zero crossing before an identified signal peak and ends at a zero crossing that after the signal peak. As another example, a signal segment may be the a portion of a signal that exceeds a threshold value. 
     In an embodiment, selected signal segments may be rescaled by a constant value. In an embodiment, selected signal segments may be nonlinearly rescaled based at least in part on a distance between a signal peak another suitable values (e.g., a characteristic value of the signal or a threshold value). 
     For the purposes of illustration, and not by way of limitation, in an embodiment disclosed herein the respiration signal may be derived from a photoplethysmograph (PPG) signal drawn from any suitable source, such as a pulse oximeter. The PPG signal may be filtered, processed or otherwise transformed before the techniques described herein are applied to the signal. A scalogram may be generated from the PPG signal data. Respiratory features may be identified within the scalogram and/or within a secondary wavelet decomposition of the scalogram. A respiration signal may be generated from these identified respiratory features. 
     In an embodiment, a normalized respiration signal may be generated from a scalogram of wavelet phase information calculated from a PPG signal. A respiration ridge representing local phase values relating to respiratory features as a function of time may be identified within the scalogram. A sinusoidal function indicative of respiration phase and having normalized height values may then be generated from these local phase values. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other features of the present disclosure, its nature and various advantages will be more apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings in which: 
         FIG. 1  shows an illustrative pulse oximetry system in accordance with an embodiment; 
         FIG. 2  is a block diagram of the illustrative pulse oximetry system of  FIG. 1  coupled to a patient in accordance with an embodiment; 
         FIGS. 3(   a ) and  3 ( b ) show illustrative views of a scalogram derived from a PPG signal in accordance with an embodiment; 
         FIG. 3(   c ) shows an illustrative scalogram derived from a signal containing two pertinent components in accordance with an embodiment; 
         FIG. 3(   d ) shows an illustrative schematic of signals associated with a ridge in  FIG. 3(   c ) and illustrative schematics of a further wavelet decomposition of these newly derived signals in accordance with an embodiment; 
         FIGS. 3(   e ) and  3 ( f ) are flow charts of illustrative steps involved in performing an inverse continuous wavelet transform in accordance with embodiments; 
         FIG. 4  is a block diagram of an illustrative continuous wavelet processing system in accordance with some embodiments; 
         FIG. 5  is an illustrative plot of a respiration signal in accordance with an embodiment; 
         FIG. 6  is another illustrative plot of a respiration signal in accordance with an embodiment; 
         FIG. 7  depicts an illustrative process for normalizing respiratory feature values of a respiration signal in accordance with an embodiment; 
         FIG. 8  depicts an illustrative process for adjusting one or more respiration signal peaks in accordance with an embodiment; and 
         FIG. 9  depicts an additional illustrative process for generating a normalized respiration signal from a scalogram in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     An oximeter is a medical device that may determine the oxygen saturation of the blood. One common type of oximeter is a pulse oximeter, which may indirectly measure the oxygen saturation of a patient&#39;s blood (as opposed to measuring oxygen saturation directly by analyzing a blood sample taken from the patient) and changes in blood volume in the skin. Ancillary to the blood oxygen saturation measurement, pulse oximeters may also be used to measure the pulse rate of the patient. Pulse oximeters typically measure and display various blood flow characteristics including, but not limited to, the oxygen saturation of hemoglobin in arterial blood. 
     An oximeter may include a light sensor that is placed at a site on a patient, typically a fingertip, toe, forehead or earlobe, or in the case of a neonate, across a foot. The oximeter may pass light using a light source through blood perfused tissue and photoelectrically sense the absorption of light in the tissue. For example, the oximeter may measure the intensity of light that is received at the light sensor as a function of time. A signal representing light intensity versus time or a mathematical manipulation of this signal (e.g., a scaled version thereof, a log taken thereof, a scaled version of a log taken thereof, etc.) may be referred to as the photoplethysmograph (PPG) signal. In addition, the term “PPG signal,” as used herein, may also refer to an absorption signal (i.e., representing the amount of light absorbed by the tissue) or any suitable mathematical manipulation thereof. The light intensity or the amount of light absorbed may then be used to calculate the amount of the blood constituent (e.g., oxyhemoglobin) being measured as well as the pulse rate and when each individual pulse occurs. 
     The light passed through the tissue is selected to be of one or more wavelengths that are absorbed by the blood in an amount representative of the amount of the blood constituent present in the blood. The amount of light passed through the tissue varies in accordance with the changing amount of blood constituent in the tissue and the related light absorption. Red and infrared wavelengths may be used because it has been observed that highly oxygenated blood will absorb relatively less red light and more infrared light than blood with a lower oxygen saturation. By comparing the intensities of two wavelengths at different points in the pulse cycle, it is possible to estimate the blood oxygen saturation of hemoglobin in arterial blood. 
     When the measured blood parameter is the oxygen saturation of hemoglobin, a convenient starting point assumes a saturation calculation based on Lambert-Beer&#39;s law. The following notation will be used herein: 
         I (λ,  t )= I   0 (λ) exp(−( sβ   0 (λ)+(1 −s )β r (λ)) l ( t ))   (1)
 
     where:
     λ=wavelength;   t=time;   I=intensity of light detected;   I o =intensity of light transmitted;   s=oxygen saturation;   β o , β t =empirically derived absorption coefficients; and   l(t)=a combination of concentration and path length from emitter to detector as a function of time.   

     The traditional approach measures light absorption at two wavelengths (e.g., red and infrared (IR)), and then calculates saturation by solving for the “ratio of ratios” as follows.
     1. First, the natural logarithm of (l) is taken (“log” will be used to represent the natural logarithm) for IR and Red   

       log  l =log I 0 −( sβ   0 +(1 −s )β r ) l    (2)
     2. (2) is then differentiated with respect to time   

     
       
         
           
             
               
                 
                   
                     
                       
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         Note in discrete time 
       
    
     
       
         
           
             
               
                 
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     where R represents the “ratio of ratios.” Solving (4) for s using (5) gives 
     
       
         
           
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         From (5), R can be calculated using two points (e.g., PPG maximum and minimum), or a family of points. One method using a family of points uses a modified version of (5). Using the relationship 
       
    
     
       
         
           
             
               
                 
                   
                     
                       
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     now (5) becomes 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
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     which defines a cluster of points whose slope of y versus x will give R where 
         x ( t )=[ I ( t   2 , λ IR )− I ( t   1 , λ IR )] I ( t   1 , λ R )
 
         y ( t )=[ I ( t   2 , λ R )− I ( t   1 , λ R )] I ( t   1 , λ IR )
 
         y ( t )= Rx ( t )   (8)
 
       FIG. 1  is a perspective view of an embodiment of a pulse oximetry system  10 . System  10  may include a sensor  12  and a pulse oximetry monitor  14 . Sensor  12  may include an emitter  16  for emitting light at two or more wavelengths into a patient&#39;s tissue. A detector  18  may also be provided in sensor  12  for detecting the light originally from emitter  16  that emanates from the patient&#39;s tissue after passing through the tissue. 
     According to another embodiment and as will be described, system  10  may include a plurality of sensors forming a sensor array in lieu of single sensor  12 . Each of the sensors of the sensor array may be a complementary metal oxide semiconductor (CMOS) sensor. Alternatively, each sensor of the array may be charged coupled device (CCD) sensor. In another embodiment, the sensor array may be made up of a combination of CMOS and CCD sensors. The CCD sensor may comprise a photoactive region and a transmission region for receiving and transmitting data whereas the CMOS sensor may be made up of an integrated circuit having an array of pixel sensors. Each pixel may have a photodetector and an active amplifier. 
     According to an embodiment, emitter  16  and detector  18  may be on opposite sides of a digit such as a finger or toe, in which case the light that is emanating from the tissue has passed completely through the digit. In an embodiment, emitter  16  and detector  18  may be arranged so that light from emitter  16  penetrates the tissue and is reflected by the tissue into detector  18 , such as a sensor designed to obtain pulse oximetry data from a patient&#39;s forehead. 
     In an embodiment, the sensor or sensor array may be connected to and draw its power from monitor  14  as shown. In another embodiment, the sensor may be wirelessly connected to monitor  14  and include its own battery or similar power supply (not shown). Monitor  14  may be configured to calculate physiological parameters based at least in part on data received from sensor  12  relating to light emission and detection. In an alternative embodiment, the calculations may be performed on the monitoring device itself and the result of the oximetry reading may be passed to monitor  14 . Further, monitor  14  may include a display  20  configured to display the physiological parameters or other information about the system. In the embodiment shown, monitor  14  may also include a speaker  22  to provide an audible sound that may be used in various other embodiments, such as for example, sounding an audible alarm in the event that a patient&#39;s physiological parameters are not within a predefined normal range. 
     In an embodiment, sensor  12 , or the sensor array, may be communicatively coupled to monitor  14  via a cable  24 . However, in other embodiments, a wireless transmission device (not shown) or the like may be used instead of or in addition to cable  24 . 
     In the illustrated embodiment, pulse oximetry system  10  may also include a multi-parameter patient monitor  26 . The monitor may be cathode ray tube type, a flat panel display (as shown) such as a liquid crystal display (LCD) or a plasma display, or any other type of monitor now known or later developed. Multi-parameter patient monitor  26  may be configured to calculate physiological parameters and to provide a display  28  for information from monitor  14  and from other medical monitoring devices or systems (not shown). For example, multiparameter patient monitor  26  may be configured to display an estimate of a patient&#39;s blood oxygen saturation generated by pulse oximetry monitor  14  (referred to as an “SpO 2 ” measurement), pulse rate information from monitor  14  and blood pressure from a blood pressure monitor (not shown) on display  28 . 
     Monitor  14  may be communicatively coupled to multi-parameter patient monitor  26  via a cable  32  or  34  that is coupled to a sensor input port or a digital communications port, respectively and/or may communicate wirelessly (not shown). In addition, monitor  14  and/or multi-parameter patient monitor  26  may be coupled to a network to enable the sharing of information with servers or other workstations (not shown). Monitor  14  may be powered by a battery (not shown) or by a conventional power source such as a wall outlet. 
       FIG. 2  is a block diagram of a pulse oximetry system, such as pulse oximetry system  10  of  FIG. 1 , which may be coupled to a patient  40  in accordance with an embodiment. Certain illustrative components of sensor  12  and monitor  14  are illustrated in  FIG. 2 . Sensor  12  may include emitter  16 , detector  18 , and encoder  42 . In the embodiment shown, emitter  16  may be configured to emit at least two wavelengths of light (e.g., RED and IR) into a patient&#39;s tissue  40 . Hence, emitter  16  may include a RED light emitting light source such as RED light emitting diode (LED)  44  and an IR light emitting light source such as IR LED  46  for emitting light into the patient&#39;s tissue  40  at the wavelengths used to calculate the patient&#39;s physiological parameters. In one embodiment, the RED wavelength may be between about 600 nm and about 700 nm, and the IR wavelength may be between about 800 nm and about 1000 nm. In embodiments where a sensor array is used in place of single sensor, each sensor may be configured to emit a single wavelength. For example, a first sensor emits only a RED light while a second only emits an IR light. 
     It will be understood that, as used herein, the term “light” may refer to energy produced by radiative sources and may include one or more of ultrasound, radio, microwave, millimeter wave, infrared, visible, ultraviolet, gamma ray or X-ray electromagnetic radiation. As used herein, light may also include any wavelength within the radio, microwave, infrared, visible, ultraviolet, or X-ray spectra, and that any suitable wavelength of electromagnetic radiation may be appropriate for use with the present techniques. Detector  18  may be chosen to be specifically sensitive to the chosen targeted energy spectrum of the emitter  16 . 
     In an embodiment, detector  18  may be configured to detect the intensity of light at the RED and IR wavelengths. Alternatively, each sensor in the array may be configured to detect an intensity of a single wavelength. In operation, light may enter detector  18  after passing through the patient&#39;s tissue  40 . Detector  18  may convert the intensity of the received light into an electrical signal. The light intensity is directly related to the absorbance and/or reflectance of light in the tissue  40 . That is, when more light at a certain wavelength is absorbed or reflected, less light of that wavelength is received from the tissue by the detector  18 . After converting the received light to an electrical signal, detector  18  may send the signal to monitor  14 , where physiological parameters may be calculated based on the absorption of the RED and IR wavelengths in the patient&#39;s tissue  40 . 
     In an embodiment, encoder  42  may contain information about sensor  12 , such as what type of sensor it is (e.g., whether the sensor is intended for placement on a forehead or digit) and the wavelengths of light emitted by emitter  16 . This information may be used by monitor  14  to select appropriate algorithms, lookup tables and/or calibration coefficients stored in monitor  14  for calculating the patient&#39;s physiological parameters. 
     Encoder  42  may contain information specific to patient  40 , such as, for example, the patient&#39;s age, weight, and diagnosis. This information may allow monitor  14  to determine, for example, patient-specific threshold ranges in which the patient&#39;s physiological parameter measurements should fall and to enable or disable additional physiological parameter algorithms. Encoder  42  may, for instance, be a coded resistor which stores values corresponding to the type of sensor  12  or the type of each sensor in the sensor array, the wavelengths of light emitted by emitter  16  on each sensor of the sensor array, and/or the patient&#39;s characteristics. In another embodiment, encoder  42  may include a memory on which one or more of the following information may be stored for communication to monitor  14 : the type of the sensor  12 ; the wavelengths of light emitted by emitter  16 ; the particular wavelength each sensor in the sensor array is monitoring; a signal threshold for each sensor in the sensor array; any other suitable information; or any combination thereof. 
     In an embodiment, signals from detector  18  and encoder  42  may be transmitted to monitor  14 . In the embodiment shown, monitor  14  may include a general-purpose microprocessor  48  connected to an internal bus  50 . Microprocessor  48  may be adapted to execute software, which may include an operating system and one or more applications, as part of performing the functions described herein. Also connected to bus  50  may be a read-only memory (ROM)  52 , a random access memory (RAM)  54 , user inputs  56 , display  20 , and speaker  22 . 
     RAM  54  and ROM  52  are illustrated by way of example, and not limitation. Any suitable computer-readable media may be used in the system for data storage. Computer-readable media are capable of storing information that can be interpreted by microprocessor  48 . This information may be data or may take the form of computer-executable instructions, such as software applications, that cause the microprocessor to perform certain functions and/or computer-implemented methods. Depending on the embodiment, such computer-readable media may include computer storage media and communication media. Computer storage media may include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media may include, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by components of the system. 
     In the embodiment shown, a time processing unit (TPU)  58  may provide timing control signals to a light drive circuitry  60 , which may control when emitter  16  is illuminated and multiplexed timing for the RED LED  44  and the IR LED  46 . TPU  58  may also control the gating-in of signals from detector  18  through an amplifier  62  and a switching circuit  64 . These signals are sampled at the proper time, depending upon which light source is illuminated. The received signal from detector  18  may be passed through an amplifier  66 , a low pass filter  68 , and an analog-to-digital converter  70 . The digital data may then be stored in a queued serial module (QSM)  72  (or buffer) for later downloading to RAM  54  as QSM  72  fills up. In one embodiment, there may be multiple separate parallel paths having amplifier  66 , filter  68 , and A/D converter  70  for multiple light wavelengths or spectra received. 
     In an embodiment, microprocessor  48  may determine the patient&#39;s physiological parameters, such as SpO 2  and pulse rate, using various algorithms and/or look-up tables based on the value of the received signals and/or data corresponding to the light received by detector  18 . Signals corresponding to information about patient  40 , and particularly about the intensity of light emanating from a patient&#39;s tissue over time, may be transmitted from encoder  42  to a decoder  74 . These signals may include, for example, encoded information relating to patient characteristics. Decoder  74  may translate these signals to enable the microprocessor to determine the thresholds based on algorithms or look-up tables stored in ROM  52 . User inputs  56  may be used to enter information about the patient, such as age, weight, height, diagnosis, medications, treatments, and so forth. In an embodiment, display  20  may exhibit a list of values which may generally apply to the patient, such as, for example, age ranges or medication families, which the user may select using user inputs  56 . 
     The optical signal through the tissue can be degraded by noise, among other sources. One source of noise is ambient light that reaches the light detector. Another source of noise is electromagnetic coupling from other electronic instruments. Movement of the patient also introduces noise and affects the signal. For example, the contact between the detector and the skin, or the emitter and the skin, can be temporarily disrupted when movement causes either to move away from the skin. In addition, because blood is a fluid, it responds differently than the surrounding tissue to inertial effects, thus resulting in momentary changes in volume at the point to which the oximeter probe is attached. 
     Noise (e.g., from patient movement) can degrade a pulse oximetry signal relied upon by a physician, without the physician&#39;s awareness. This is especially true if the monitoring of the patient is remote, the motion is too small to be observed, or the doctor is watching the instrument or other parts of the patient, and not the sensor site. Processing pulse oximetry (i.e., PPG) signals may involve operations that reduce the amount of noise present in the signals or otherwise identify noise components in order to prevent them from affecting measurements of physiological parameters derived from the PPG signals. 
     It will be understood that the present disclosure is applicable to any suitable signals and that PPG signals are used merely for illustrative purposes. Those skilled in the art will recognize that the present disclosure has wide applicability to other signals including, but not limited to other biosignals (e.g., electrocardiogram, electroencephalogram, electrogastrogram, electromyogram, heart rate signals, pathological sounds, ultrasound, or any other suitable biosignal), dynamic signals, non-destructive testing signals, condition monitoring signals, fluid signals, geophysical signals, astronomical signals, electrical signals, financial signals including financial indices, sound and speech signals, chemical signals, meteorological signals including climate signals, and/or any other suitable signal, and/or any combination thereof 
     In one embodiment, a PPG signal may be transformed using a continuous wavelet transform. Information derived from the transform of the PPG signal (i.e., in wavelet space) may be used to provide measurements of one or more physiological parameters. 
     The continuous wavelet transform of a signal x(t) in accordance with the present disclosure may be defined as 
     
       
         
           
             
               
                 
                   
                     T 
                      
                     
                       ( 
                       
                         a 
                         , 
                         b 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         a 
                       
                     
                      
                     
                       
                         ∫ 
                         
                           - 
                           ∞ 
                         
                         
                           + 
                           ∞ 
                         
                       
                        
                       
                         
                           x 
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                         
                           
                             ψ 
                             * 
                           
                            
                           
                             ( 
                             
                               
                                 t 
                                 - 
                                 b 
                               
                               a 
                             
                             ) 
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     where ψ*(t) is the complex conjugate of the wavelet function ψ(t), a is the dilation parameter of the wavelet and b is the location parameter of the wavelet. The transform given by equation ( 9 ) may be used to construct a representation of a signal on a transform surface. The transform may be regarded as a time-scale representation. Wavelets are composed of a range of frequencies, one of which may be denoted as the characteristic frequency of the wavelet, where the characteristic frequency associated with the wavelet is inversely proportional to the scale a. One example of a characteristic frequency is the dominant frequency. Each scale of a particular wavelet may have a different characteristic frequency. The underlying mathematical detail required for the implementation within a time-scale can be found, for example, in Paul S. Addison, The Illustrated Wavelet Transform Handbook (Taylor &amp; Francis Group 2002), which is hereby incorporated by reference herein in its entirety. 
     The continuous wavelet transform decomposes a signal using wavelets, which are generally highly localized in time. The continuous wavelet transform may provide a higher resolution relative to discrete transforms, thus providing the ability to garner more information from signals than typical frequency transforms such as Fourier transforms (or any other spectral techniques) or discrete wavelet transforms. Continuous wavelet transforms allow for the use of a range of wavelets with scales spanning the scales of interest of a signal such that small scale signal components correlate well with the smaller scale wavelets and thus manifest at high energies at smaller scales in the transform. Likewise, large scale signal components correlate well with the larger scale wavelets and thus manifest at high energies at larger scales in the transform. Thus, components at different scales may be separated and extracted in the wavelet transform domain. Moreover, the use of a continuous range of wavelets in scale and time position allows for a higher resolution transform than is possible relative to discrete techniques. 
     In addition, transforms and operations that convert a signal or any other type of data into a spectral (i.e., frequency) domain necessarily create a series of frequency transform values in a two-dimensional coordinate system where the two dimensions may be frequency and, for example, amplitude. For example, any type of Fourier transform would generate such a two-dimensional spectrum. In contrast, wavelet transforms, such as continuous wavelet transforms, are required to be defined in a three-dimensional coordinate system and generate a surface with dimensions of time, scale and, for example, amplitude. Hence, operations performed in a spectral domain cannot be performed in the wavelet domain; instead the wavelet surface must be transformed into a spectrum (i.e., by performing an inverse wavelet transform to convert the wavelet surface into the time domain and then performing a spectral transform from the time domain). Conversely, operations performed in the wavelet domain cannot be performed in the spectral domain; instead a spectrum must first be transformed into a wavelet surface (i.e., by performing an inverse spectral transform to convert the spectral domain into the time domain and then performing a wavelet transform from the time domain). Nor does a cross-section of the three-dimensional wavelet surface along, for example, a particular point in time equate to a frequency spectrum upon which spectral-based techniques may be used. At least because wavelet space includes a time dimension, spectral techniques and wavelet techniques are not interchangeable. It will be understood that converting a system that relies on spectral domain processing to one that relies on wavelet space processing would require significant and fundamental modifications to the system in order to accommodate the wavelet space processing (e.g., to derive a representative energy value for a signal or part of a signal requires integrating twice, across time and scale, in the wavelet domain while, conversely, one integration across frequency is required to derive a representative energy value from a spectral domain). As a further example, to reconstruct a temporal signal requires integrating twice, across time and scale, in the wavelet domain while, conversely, one integration across frequency is required to derive a temporal signal from a spectral domain. It is well known in the art that, in addition to or as an alternative to amplitude, parameters such as energy density, modulus, phase, among others may all be generated using such transforms and that these parameters have distinctly different contexts and meanings when defined in a two-dimensional frequency coordinate system rather than a three-dimensional wavelet coordinate system. For example, the phase of a Fourier system is calculated with respect to a single origin for all frequencies while the phase for a wavelet system is unfolded into two dimensions with respect to a wavelet&#39;s location (often in time) and scale. 
     The energy density function of the wavelet transform, the scalogram, is defined as 
         S ( a,b )=| T ( a,b )| 2    (10)
 
     where ‘∥’ is the modulus operator. The scalogram may be rescaled for useful purposes. 
     One common rescaling is defined as 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       R 
                     
                      
                     
                       ( 
                       
                         a 
                         , 
                         b 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
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                           T 
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                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     and is useful for defining ridges in wavelet space when, for example, the Morlet wavelet is used. Ridges are defined as the locus of points of local maxima in the plane. Any reasonable definition of a ridge may be employed in the method. Also included as a definition of a ridge herein are paths displaced from the locus of the local maxima. A ridge associated with only the locus of points of local maxima in the plane are labeled a “maxima ridge”. 
     For implementations requiring fast numerical computation, the wavelet transform may be expressed as an approximation using Fourier transforms. Pursuant to the convolution theorem, because the wavelet transform is the cross-correlation of the signal with the wavelet function, the wavelet transform may be approximated in terms of an inverse FFT of the product of the Fourier transform of the signal and the Fourier transform of the wavelet for each required a scale and then multiplying the result by √{square root over (a)}. 
     In the discussion of the technology which follows herein, the “scalogram” may be taken to include all suitable forms of rescaling including, but not limited to, the original unscaled wavelet representation, linear rescaling, any power of the modulus of the wavelet transform, or any other suitable rescaling. In addition, for purposes of clarity and conciseness, the term “scalogram” shall be taken to mean the wavelet transform, T(a,b) itself, or any part thereof. For example, the real part of the wavelet transform, the imaginary part of the wavelet transform, the phase of the wavelet transform, any other suitable part of the wavelet transform, or any combination thereof is intended to be conveyed by the term “scalogram”. 
     A scale, which may be interpreted as a representative temporal period, may be converted to a characteristic frequency of the wavelet function. The characteristic frequency associated with a wavelet of arbitrary a scale is given by 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       f 
                       c 
                     
                     a 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     where f C , the characteristic frequency of the mother wavelet (i.e., at a=1), becomes a scaling constant and f is the representative or characteristic frequency for the wavelet at arbitrary scale a. 
     Any suitable wavelet function may be used in connection with the present disclosure. One of the most commonly used complex wavelets, the Morlet wavelet, is defined as: 
       ψ( t )=π −1/4 ( e   i2πf     0     t   −e   −(2πf     0     )     2     /2 ) e   −t     2     /2    (13)
 
     where f 0  is the central frequency of the mother wavelet. The second term in the parenthesis is known as the correction term, as it corrects for the non-zero mean of the complex sinusoid within the Gaussian window. In practice, it becomes negligible for values of f 0 &gt;&gt;0 and can be ignored, in which case, the Morlet wavelet can be written in a simpler form as 
     
       
         
           
             
               
                 
                   
                     ψ 
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         π 
                         
                           1 
                           / 
                           4 
                         
                       
                     
                      
                     
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                         t 
                       
                     
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                           - 
                           
                             t 
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                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     This wavelet is a complex wave within a scaled Gaussian envelope. While both definitions of the Morlet wavelet are included herein, the function of equation (14) is not strictly a wavelet as it has a non-zero mean (i.e., the zero frequency term of its corresponding energy spectrum is non-zero). However, it will be recognized by those skilled in the art that equation (14) may be used in practice with f 0 &gt;&gt;0 with minimal error and is included (as well as other similar near wavelet functions) in the definition of a wavelet herein. A more detailed overview of the underlying wavelet theory, including the definition of a wavelet function, can be found in the general literature. Discussed herein is how wavelet transform features may be extracted from the wavelet decomposition of signals. For example, wavelet decomposition of PPG signals may be used to provide clinically useful information within a medical device. 
     Pertinent repeating features in a signal give rise to a time-scale band in wavelet space or a rescaled wavelet space. For example, the pulse component of a PPG signal produces a dominant band in wavelet space at or around the pulse frequency.  FIGS. 3(   a ) and ( b ) show two views of an illustrative scalogram derived from a PPG signal, according to an embodiment. The figures show an example of the band caused by the pulse component in such a signal. The pulse band is located between the dashed lines in the plot of  FIG. 3(   a ). The band is formed from a series of dominant coalescing features across the scalogram. This can be clearly seen as a raised band across the transform surface in  FIG. 3(   b ) located within the region of scales indicated by the arrow in the plot (corresponding to 60 beats per minute). The maxima of this band with respect to scale is the ridge. The locus of the ridge is shown as a black curve on top of the band in  FIG. 3(   b ). By employing a suitable rescaling of the scalogram, such as that given in equation (11), the ridges found in wavelet space may be related to the instantaneous frequency of the signal. In this way, the pulse rate may be obtained from the PPG signal. Instead of rescaling the scalogram, a suitable predefined relationship between the scale obtained from the ridge on the wavelet surface and the actual pulse rate may also be used to determine the pulse rate. 
     By mapping the time-scale coordinates of the pulse ridge onto the wavelet phase information gained through the wavelet transform, individual pulses may be captured. In this way, both times between individual pulses and the timing of components within each pulse may be monitored and used to detect heart beat anomalies, measure arterial system compliance, or perform any other suitable calculations or diagnostics. Alternative definitions of a ridge may be employed. Alternative relationships between the ridge and the pulse frequency of occurrence may be employed. 
     As discussed above, pertinent repeating features in the signal give rise to a time-scale band in wavelet space or a rescaled wavelet space. For a periodic signal, this band remains at a constant scale in the time-scale plane. For many real signals, especially biological signals, the band may be non-stationary; varying in scale, amplitude, or both over time.  FIG. 3(   c ) shows an illustrative schematic of a wavelet transform of a signal containing two pertinent components leading to two bands in the transform space, according to an embodiment. These bands are labeled band A and band B on the three-dimensional schematic of the wavelet surface. In this embodiment, the band ridge is defined as the locus of the peak values of these bands with respect to scale. For purposes of discussion, it may be assumed that band B contains the signal information of interest. This will be referred to as the “primary band”. In addition, it may be assumed that the system from which the signal originates, and from which the transform is subsequently derived, exhibits some form of coupling between the signal components in band A and band B. When noise or other erroneous features are present in the signal with similar spectral characteristics of the features of band B then the information within band B can become ambiguous (i.e., obscured, fragmented or missing). In this case, the ridge of band A may be followed in wavelet space and extracted either as an amplitude signal or a scale signal which will be referred to as the “ridge amplitude perturbation” (RAP) signal and the “ridge scale perturbation” (RSP) signal, respectively. The RAP and RSP signals may be extracted by projecting the ridge onto the time-amplitude or time-scale planes, respectively. The top plots of  FIG. 3(   d ) show a schematic of the RAP and RSP signals associated with ridge A in  FIG. 3(   c ). Below these RAP and RSP signals are schematics of a further wavelet decomposition of these newly derived signals. This secondary wavelet decomposition allows for information in the region of band B in  FIG. 3(   c ) to be made available as band C and band D. The ridges of bands C and D may serve as instantaneous time-scale characteristic measures of the signal components causing bands C and D. This technique, which will be referred to herein as secondary wavelet feature decoupling (SWFD), may allow information concerning the nature of the signal components associated with the underlying physical process causing the primary band B ( FIG. 3(   c )) to be extracted when band B itself is obscured in the presence of noise or other erroneous signal features. 
     In some instances, an inverse continuous wavelet transform may be desired, such as when modifications to a scalogram (or modifications to the coefficients of a transformed signal) have been made in order to, for example, remove artifacts. In one embodiment, there is an inverse continuous wavelet transform which allows the original signal to be recovered from its wavelet transform by integrating over all scales and locations, a and b: 
     
       
         
           
             
               
                 
                   
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                   15 
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     which may also be written as: 
     
       
         
           
             
               
                 
                   
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                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     where C g  is a scalar value known as the admissibility constant. It is wavelet type dependent and may be calculated from: 
     
       
         
           
             
               
                 
                   
                     C 
                     g 
                   
                   = 
                   
                     
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                                 ψ 
                                 ^ 
                               
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                   ( 
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                   ) 
                 
               
             
           
         
       
     
       FIG. 3(   e ) is a flow chart of illustrative steps that may be taken to perform an inverse continuous wavelet transform in accordance with the above discussion. An approximation to the inverse transform may be made by considering equation (15) to be a series of convolutions across scales. It shall be understood that there is no complex conjugate here, unlike for the cross correlations of the forward transform. As well as integrating over all of a and b for each time t, this equation may also take advantage of the convolution theorem which allows the inverse wavelet transform to be executed using a series of multiplications.  FIG. 3(   f ) is a flow chart of illustrative steps that may be taken to perform an approximation of an inverse continuous wavelet transform. It will be understood that any other suitable technique for performing an inverse continuous wavelet transform may be used in accordance with the present disclosure. 
       FIG. 4  is an illustrative continuous wavelet processing system in accordance with an embodiment. In this embodiment, input signal generator  410  generates an input signal  416 . As illustrated, input signal generator  410  may include oximeter  420  coupled to sensor  418 , which may provide as input signal  416 , a PPG signal. It will be understood that input signal generator  410  may include any suitable signal source, signal generating data, signal generating equipment, or any combination thereof to produce signal  416 . Signal  416  may be any suitable signal or signals, such as, for example, biosignals (e.g., electrocardiogram, electroencephalogram, electrogastrogram, electromyogram, heart rate signals, pathological sounds, ultrasound, or any other suitable biosignal), dynamic signals, non-destructive testing signals, condition monitoring signals, fluid signals, geophysical signals, astronomical signals, electrical signals, financial signals including financial indices, sound and speech signals, chemical signals, meteorological signals including climate signals, and/or any other suitable signal, and/or any combination thereof 
     In this embodiment, signal  416  may be coupled to processor  412 . Processor  412  may be any suitable software, firmware, and/or hardware, and/or combinations thereof for processing signal  416 . For example, processor  412  may include one or more hardware processors (e.g., integrated circuits), one or more software modules, computer-readable media such as memory, firmware, or any combination thereof. Processor  412  may, for example, be a computer or may be one or more chips (i.e., integrated circuits). Processor  412  may perform the calculations associated with the continuous wavelet transforms of the present disclosure as well as the calculations associated with any suitable interrogations of the transforms. Processor  412  may perform any suitable signal processing of signal  416  to filter signal  416 , such as any suitable band-pass filtering, adaptive filtering, closed-loop filtering, and/or any other suitable filtering, and/or any combination thereof. 
     Processor  412  may be coupled to one or more memory devices (not shown) or incorporate one or more memory devices such as any suitable volatile memory device (e.g., RAM, registers, etc.), non-volatile memory device (e.g., ROM, EPROM, magnetic storage device, optical storage device, flash memory, etc.), or both. The memory may be used by processor  412  to, for example, store data corresponding to a continuous wavelet transform of input signal  416 , such as data representing a scalogram. In one embodiment, data representing a scalogram may be stored in RAM or memory internal to processor  412  as any suitable three-dimensional data structure such as a three-dimensional array that represents the scalogram as energy levels in a time-scale plane. Any other suitable data structure may be used to store data representing a scalogram. 
     Processor  412  may be coupled to output  414 . Output  414  may be any suitable output device such as, for example, one or more medical devices (e.g., a medical monitor that displays various physiological parameters, a medical alarm, or any other suitable medical device that either displays physiological parameters or uses the output of processor  412  as an input), one or more display devices (e.g., monitor, PDA, mobile phone, any other suitable display device, or any combination thereof), one or more audio devices, one or more memory devices (e.g., hard disk drive, flash memory, RAM, optical disk, any other suitable memory device, or any combination thereof), one or more printing devices, any other suitable output device, or any combination thereof. 
     It will be understood that system  400  may be incorporated into system  10  ( FIGS. 1 and 2 ) in which, for example, input signal generator  410  may be implemented as parts of sensor  12  and monitor  14  and processor  412  may be implemented as part of monitor  14 . 
       FIG. 5  is an illustrative plot  500  of a respiration signal  505 . Respiration signal  505  may indicate the breathing patterns of a patient over time. Plot  500  displays time on the x-axis and signal amplitude values of respiration signal  505  on the y-axis. Plot  500  may be displayed using any suitable display device such as, for example, monitor  20  ( FIG. 1 ), display  28  ( FIG. 1 ), a PDA, a mobile device, or any other suitable display device. Additionally, plot  500  may be displayed on multiple display devices. 
     Respiration signal  505  may be obtained using a sensor capable of measuring the respiration of a patient, such as patient  40  ( FIG. 2 ). For example, the respiration of a patient may be measured using a flow meter or a chest band sensor. Respiration signal  505  may also be derived from other biological signals (i.e., biosignals) captured by one or more sensors of a suitable biosignal measurement system. For example, respiration signal  505  may be derived from PPG signal data received from a pulse oximetry system such as pulse oximetry system  10  ( FIG. 1 ). Respiration signal  505  may also be derived from other biosignals including transthoracic impedance signals, capnograph signals, nasal thermistor signals, and/or electrocardiogram (EKG) signals. The derivation of respiration signal  505  from a PPG signal or other suitable biosignal will be described in more detail below. Although, the techniques disclosed herein are described in terms of a respiration signal derived from a PPG signal, the disclosed techniques may be applied to any respiration signal or any other biosignals where cyclic phenomena are captured by the measurement system. 
     Respiration signal  505  may exhibit an oscillatory behavior versus time. The size, shape, and frequency of respiration signal  505  may be indicative of the breaths or breathing cycle of a patient, such as patient  40  ( FIG. 2 ), and/or may be used determine the respiration rate of the patient. Respiration signal  505  may be a processed version of a preliminary respiration signal obtained from a sensor or derived from a suitable biosignal. The preliminary respiration signal may contain erroneous or otherwise undesirable artifacts due to, for example, patient movement, equipment failure, and/or various noise sources. For example, cable  24 , cable  32 , and/or cable  34  (all of  FIG. 1 ) may malfunction or become loosened from the equipment to which it is connected. Further, sensor  12  ( FIG. 1 ), or any constituent component of sensor  12  ( FIG. 1 ) (for example, emitter  16  ( FIG. 1 ) and/or detector  18  ( FIG. 1 )) may malfunction and/or become loosened. Additionally, noise sources may produce inconsistent features in a PPG signal or other biosignal from which respiration signal  505  was derived. Possible sources of noise include thermal noise, shot noise, flicker noise, burst noise, and/or electrical noise caused by light pollution. These and other noise sources may be introduced, for example, through sensor  12  ( FIG. 1 ), and/or cables  24 ,  32 , and  34  (all of  FIG. 1 ). These and/or other phenomena may be present in a system such as pulse oximetry system  10  ( FIG. 1 ), and thus may introduce inconsistent features into the measured PPG signal and in turn may introduce inconsistent features into respiration signal  505 . 
     As shown in plot  500 , respiration signal  505  may be substantially free of these erroneous and otherwise undesirable artifacts. The effect of these artifacts on a respiration signal may be reduced or eliminated by processing the underlying biosignal (e.g., a PPG signal) from which respiration signal  505  is derived, by the processing techniques used to derive respiration signal  505  from the biosignal and/or by processing a preliminary respiration signal to obtain respiration signal  505 . Each of these processing steps may be implemented in a pulse oximetry system such as pulse oximetry system  10  ( FIG. 1 ) and may be carried out using a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ). However, even when these artifacts are reduced or eliminated, respiration signal  505  may still contain respiratory features (e.g., signal peaks) having a wide range of amplitude values. It may be advantageous to reduce the range of these amplitude values in respiration signal  505  in order to improve the interpretation and subsequent analysis of this signal and/or to obtain additional respiration parameters such as respiration rate. For example, one or more large signal peaks in respiration signal  505  may adversely effect the respiration rate determined from the signal. 
     Plot  500  of  FIG. 5  includes upper threshold  510  to reduce the amplitude variations in respiration signal  505 . Signal peaks having amplitude values that are above upper threshold  510  may be reduced. These signal peaks may be reduced to amplitude values that are closer to the threshold value, closer to a mean or median signal peak value for respiration signal  505  or closer to another predetermined value. For example, signal peaks  511 ,  512 ,  513 , and  514  all have amplitude values that exceed upper threshold  510 . These signal peaks may therefore be reduced to the values of adjusted signal peaks  511   a ,  512   a ,  513   a , and  514   a , which may be substantially equal to the value of upper threshold  510 . 
       FIG. 6  is an illustrative plot  600  of a respiration signal  605  which is similar to plot  500  of  FIG. 5  and includes additional, lower threshold  620 . Signal peaks  611 ,  612 ,  613 , and  614  all have amplitude values that exceed upper threshold  610  and may therefore be reduced to the values of adjusted signal peaks  611   a ,  612   a ,  613   a , and  614   a . Additionally or alternatively, signal peaks  621 ,  622 ,  623 , and  624  all have amplitude values that are less than upper threshold  610  and that exceed lower threshold  620 . The amplitude values of these signal peaks may be increased to the values of adjusted signal peaks  621   a ,  622   a ,  623   a , and  624   a . According to this example, amplitude values of signal peaks that exceed upper threshold  610  are reduced and signal peaks having values between lower threshold  620  and upper threshold  610  are be increased. In this manner, signal peaks having values both greater than and less than the value of upper threshold  610  may be adjusted closer to a single amplitude value, i.e., the value of upper threshold  610 . Signal peaks having amplitude values that are less than lower threshold  620  may remain unchanged to prevent erroneously small features from being increased in amplitude. In another example, upper and lower signal threshold values may be set such that signal peak values that exceed an upper threshold value or that are less than a lower threshold value may be adjusted closer to a value between the two threshold values (e.g., a mean value). Signals peak values that are between these two threshold values may remain unchanged. Additionally, a third, minimum threshold value may prevent erroneously small features from being increased in amplitude. 
     Process  700  (depicted in  FIG. 7 ) illustrates exemplary techniques for reducing amplitude variations in respiration signals  505  and  605  by normalizing the peak values of these signals based on one or more threshold values. Normalizing signal peaks within respiration signals  505  and  605  may reduce the amplitude variations of these respiration signal may improve and/or simplify the subsequent processing of these respiration signals. For example, normalizing signal peaks within respiration signals  505  and  605  may aid in the determination of respiration rate information from these signals. 
       FIG. 7  depicts an illustrative process  700  for normalizing respiratory feature amplitude values of a respiration signal (or parts of a respiration signal), e.g., respiration signal  505  ( FIG. 5 ) or respiration signal  605  ( FIG. 6 ). Process  700  may be implemented in a pulse oximetry system such as pulse oximetry system  10  ( FIG. 1 ), and the steps of process  700  may be carried out using a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ). 
     Process  700  may start at step  710 . At step  720 , process  700  may obtain a respiration signal. The respiration signal obtained in step  720  may be obtained using a sensor capable of measuring the respiration of a patient, such as patient  40  ( FIG. 2 ). For example, the respiration of a patient may be measured using a flow meter or a chest band sensor. The respiration signal obtained in step  720  may also be derived from other biological signals (i.e., biosignals) captured by one or more sensors of a suitable biosignal measurement system. For example, respiration signal  505  may be derived from PPG signal data received from a pulse oximetry system such as pulse oximetry system  10  ( FIG. 1 ) using a sensor such as sensor  12  ( FIG. 1 ) to measure biological characteristics of a patient such as patient  40  ( FIG. 2 ). Respiration signal  505  may also be derived from other biosignals including transthoracic impedance signals, capnograph signals, nasal thermistor signals, and/or electrocardiogram (EKG) signals. The respiration signal and/or one or more signals that may be used to derive the respiration signal may be real-time signals or may be signals previously received and stored in memory, for example, ROM  52  ( FIG. 2 ) or RAM  54  ( FIG. 2 ). 
     In an embodiment, the respiration signal obtained at step  720  may be derived from a PPG signal. The PPG signal may be obtained by processing another, preliminary PPG signal. For example, a preliminary PPG signals may be obtained using, e.g., sensor  12  ( FIG. 1 ) and processed using a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ) in a system similar or identical to pulse oximetry system  10  ( FIG. 1 ). For example, the preliminary signal may be processed using low-pass filters, noise-component removal techniques, and/or interpolation methods, that may remove various undesirable artifacts that may be present in the preliminary signal. As another example, one or more preliminary PPG signals may be selected and mirrored to create the PPG signal used to derive a reparation signal using techniques similar or identical to those described in Watson, U.S. Provisional Application No. 61/077,092, filed Jun. 30, 2008, entitled “Systems and Method for Detecting Pulses,” and McGonigle et al., U.S. application Ser. No. 12/437,317, filed May 7, 2009, entitled “Concatenated Scalograms,” which are incorporated by reference herein in their entirety. As yet another example, a preliminary PPG signal may be analyzed to calculate regions having at least a threshold level of stability and/or consistency using techniques similar or identical to those described in Watson et al., U.S. application Ser. No. 12/437,326, filed May 7, 2009—entitled “ Consistent Signal Selection By Signal Segment Selection Techniques,” which is incorporated by reference herein in its entirety. 
     The respiration signal obtained in step  720  may be derived from a PPG signal by generating a scalogram from a received PPG signal. For example, a scalogram may be derived using the same method (e.g., using continuous wavelet transforms) that was used to derive the scalograms shown in  FIGS. 3(   a ),  3 ( b ), and  3 ( c ). The scalogram of the wavelet transform may be generated or otherwise obtained using, for example a processor such as processor  412  ( FIG. 4)  or microprocessor  48  ( FIG. 2 ). In addition to the scalogram, other parts of the wavelet transform may be determined. For example, the transform modulus, phase, real, and/or imaginary parts may be generated in addition to the scalogram. 
     The resultant scalogram may include bands and ridges corresponding to at least one area of increased energy. A respiration band of the scalogram may generally reflect the breathing pattern of a patient, e.g., patient  40  ( FIG. 2 ). These bands may be extracted from the scalogram using, for example, a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ), using any suitable method. The respiration band of the scalogram may be identified using characteristics of the scalogram including the energy and structure of the scalogram, and the signal-to-noise levels in various regions of scalogram. In one embodiment, this information may be calculated one or more times using different time-window sizes. The number and type of time-window sizes that are used may depend on the anticipated respiration rate, the available computational resources (e.g., the amount of ROM  52  ( FIG. 2 ) and/or RAM  54  ( FIG. 2 ) and the speed of processor  412  ( FIG. 4 ) and/or microprocessor  48  (FIG.  2 )), as well as on possible input derived from user inputs  56  ( FIG. 2 ). 
     The respiration signal may be derived from the amplitude and/or scale modulation observed in the respiration band (e.g., respiration band B in  FIG. 3(   c )). The respiration signal may also may be derived after further analysis of the scalogram including, for example, secondary wavelet feature decoupling. This secondary wavelet feature decoupling of a ridge allows for information concerning the band of interest (e.g., respiration band B in  FIG. 3(   c )) to be made available as secondary bands (e.g., band C and band D in  FIG. 3(   d )). The ridges of the secondary bands may serve as instantaneous time-scale characteristic measures of the underlying signal components causing the secondary bands, which may be useful in analyzing the signal component associated with the underlying physical process causing the primary band of interest (e.g., the respiration band B) when band B itself may be obscured. By extracting and further analyzing a respiration band in the scalogram, a respiration signal may be extracted from the scalogram when the respiration band itself is, for example, obscured in the presence of noise or other erroneous signal features. 
     At step  730  signal peaks may be identified from the respiration signal obtained in step  720 . Signal peaks may be found, e.g., using any suitable signal processing technique, including a zero-crossing technique, a root-finding technique, an analytic curve-fitting technique, and/or a numerical analysis of the derivatives of the selected portion of the signal. These and other techniques may be implemented in pulse oximetry system  10  ( FIG. 1 ) by processor  412  ( FIG. 4 ), microprocessor  48  ( FIG. 2 ), ROM  52  ( FIG. 2 ), and/or RAM  54  ( FIG. 2 ). Additionally, the parameters that may be used by suitable signal processing techniques, e.g,. tolerance values and sensitivity levels, may be controlled by a user or patient using, e.g., using user inputs  56  ( FIG. 2 ). Signal peaks that are identified may be displayed, for example, on monitor  26  ( FIG. 1 ) or display  20  or  28  (both of  FIG. 1 ). Alternatively, a portion of the respiration signal generated at step  730  may be displayed on a monitor, and a user may choose or otherwise influence which peaks are selected using, for example, user inputs  56  ( FIG. 2 ). 
     At step  740  one or more signal peak thresholds may be selected or determined. Signal peak thresholds may calculated using any suitable signal processing and analysis techniques. For example, signal peak thresholds may be related to a mean, median, mode, range, standard deviation, or percentile of the signal peaks identified at step  730 . Signal peak threshold values may be determined based on an initial set of signal peak values. Signal peak thresholds may then be replaced or updated periodically or continuously based on newer incoming signal peak values. Alternatively, signal peak thresholds may be set to predetermined values based on historical or idealized respiration signal data or based on any other suitable data. These and other techniques may be implemented in pulse oximetry system  10  ( FIG. 1 ) by processor  412  ( FIG. 4 ), microprocessor  48  ( FIG. 2 ), ROM  52  ( FIG. 2 ), and/or RAM  54  ( FIG. 2 ). Additionally, the parameters that may be used by suitable signal processing techniques, e.g,. tolerance values and sensitivity levels, may be controlled by a user or patient using, e.g., using user inputs  56  ( FIG. 2 ). Signal peak thresholds may be displayed, for example, on monitor  26  ( FIG. 1 ) or display  20  or  28  (both of  FIG. 1 ). Alternatively, the portion of the respiration signal obtained in step  720  may be displayed on a monitor, and a user may choose or otherwise influence signal peak thresholds using, for example, user inputs  56  ( FIG. 2 ). 
     Illustrative plot  500  ( FIG. 5 ) includes a single, upper threshold  510 . Signal peaks that exceed the upper threshold value may be reduced. Illustrative plot  600  ( FIG. 6 ) includes an additional, lower threshold  620 . Signal peaks that exceed the lower threshold value may be increased, but signal peaks that have amplitudes below the lower threshold may be left unchanged. A minimum threshold (not illustrated) may reduce or eliminate signal peaks that have amplitudes below the minimum threshold values or may prevent signal peaks below this minimum threshold from being modified. Other threshold types may also be provided. The number and type of signal peak thresholds used to normalize respiration features within a respiration signal may be determined by processor  412  ( FIG. 4 ), microprocessor  48  ( FIG. 2 ) based on any suitable signal processing and analysis techniques. For example, the particular type of signal peak thresholds to be used may be determined based on the respiration signal to be processed. Additionally, the number and type of signal peak thresholds used to process a respiration signal may be controlled by a user or patient using, e.g., using user inputs  56  ( FIG. 2 ). One or more signal peak thresholds may be displayed, for example, on monitor  26  ( FIG. 1 ) or display  20  or  28  (both of  FIG. 1 ) and the user may choose or otherwise the number and type of signal peak thresholds using, for example, user inputs  56  ( FIG. 2 ). 
     At step  750 , one or more the signal peaks identified in step  730  may be adjusted based on the signal peak thresholds determined in step  740 . The signal adjustment may be performed by a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ). For example, signal peaks that exceed an upper threshold value may be reduced in value and/or signal peaks that exceed a lower threshold may be increased in value. These adjustments may be used to provide a normalized respiration signal. Alternatively or additionally, the adjustments may be made within the one or more scalograms used to generate the original respiration signal. The adjusted scalograms may be processed further to determine or estimate additional information. For example, two or more scalograms having adjusted respiratory features may be concatenated together and processed to improve the computation of information such as respiration information using techniques similar or identical to those described in McGonigle et al., U.S. application Ser. No. 12/437,317, filed May 7, 2009, entitled “Concatenated Scalograms,” which was previously incorporated by reference herein. 
     One approach for modifying the value of an identified respiration signal peak is to linearly rescale a signal segment associated with the signal peak. Referring to respiratory signal  505  ( FIG. 5 ), signal peak  511  exceeds upper threshold  510 . Therefore, a signal segment defined by the zero crossing (or any other suitable points) before and after signal peak  511 , i.e., points  511   b  and  511   c , may be rescaled by a constant factor (less than unity). In an embodiment, the constant factor may be set to a value such that the adjusted signal peak (e.g.,  511   a ) for a given signal peak (e.g.,  511   a ) is less than or equal to the signal peak threshold value or any other suitable value (e.g., a mean value). This value may be set such that all adjusted peak values will be similar. Alternatively, the same constant factor may be used irrespective of the actual signal peak value. In an embodiment, only the portion of the signal that crosses a threshold may be rescaled. For example, referring to respiratory signal  505  ( FIG. 5 ) and according to this embodiment, only the respiration signal segment between signal points  511   d  and  511   e  may be adjusted. In an embodiment, a nonlinear rescaling value may be used whereby the change in value of a respiration signal segment associated with a signal peak may be related in some way to the distance between the signal peak value and an average value of the signal. Nonlinear rescaling values may also be related to a distance between a signal peak and, for example, the threshold value, a desired value, or another predetermined value. The nonlinear relationship may be smoothly nonlinear or may be made up of discreet linear scaling factor values. 
     At step  760  a respiration parameter may be generated based on the normalized respiration signal adjusted in step  750 . For example, a respiration rate may be determined or estimated from the adjusted respiration signal using any suitable approach. The respiration rate may be represented by a number from 1 to 100, where a larger number indicates a larger respiration rate (any other suitable number range could be used instead). The determination of the respiration rate may be performed, for example, by processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ), and may additionally depend on parameters entered by a user through user inputs  56  ( FIG. 2 ). To estimate a respiration rate the processor may use, for example, maximum-likelihood techniques to combine data when the prior probability of a given respiration rate is known, and Neyman-Pearson combining techniques may be used when the prior probability of a given respiration rate is unknown. 
     At step  770  the respiration parameter determined or estimated from the respiration signal in step  760  may be reported. For example, a respiration rate may be reported by generating an audible alert or, for example, using speaker  22  ( FIG. 2 ) as well as possibly through other audio devices, generating an on-screen message, for example, on display  20  ( FIG. 1 ) or display  28  ( FIG. 1 ), generating a pager message, a text message, or a telephone call, for example, using a wireless connection embedded or attached to a system such as system  10  ( FIG. 1 ), activating a secondary or backup sensor or sensor array, for example, connected through a wire or wirelessly to monitor  14  ( FIG. 1 ), or regulating the automatic administration medicine, for example, which is controlled in part or fully through a system such as system  10  ( FIG. 1 ). Additionally, the respiration rate may be reported on a display such as display  20  ( FIG. 1 ) or display  28  ( FIG. 1 ) in graphical form using, for example, a bar graph or histogram. The respiration parameter may also be reported to one or more other processes, for example, to be used as part of or to improve the reliability of other measurements or calculations within a system such as pulse oximetry system  10  ( FIG. 1 ). 
       FIG. 8  depicts an illustrative process for adjusting one or more signal peaks in a signal, e.g., respiration signal  505  ( FIG. 5 ), in accordance with some embodiments. Process  800  may be implemented in a pulse oximetry system such as pulse oximetry system  10  ( FIG. 1 ), and the steps of process  800  may be carried out using a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ). Process  800  may correspond to a further embodiment of process  700 , and more particularly, may correspond to a further embodiment of step  750  of  FIG. 7 . Process  800  may start at step  810 . At step  810 , a first signal peak is selected. For example, at step  810 , process  800  may select one of the signal peaks of a respiration signal identified by process  700  ( FIG. 7 ) at step  730 . The first signal peak may correspond to the first-occurring signal peak in time, e.g. signal peak  511  ( FIG. 5 ) of respiration signal  505 , and/or it may correspond to the first signal peak found through a suitable signal processing algorithm, such as an extrema-finding algorithm. Once the location of a first peak has been found, at step  810  an amplitude value of the first signal peak may be determined. 
     At step  830 , it is determined whether the signal peak crosses a threshold value. The value of the signal peak may be compared to one or more signal peak threshold values determined by process  700  ( FIG. 7 ) at step  750 . For example, for respiration signal  505  ( FIG. 5 ) it may be determined that signal peak  511  exceeds threshold  510 . As another example, for respiration signal  605  ( FIG. 6 ) it may be determined that signal peak  621  exceeds threshold  620 . Signal peak  611  exceeds both thresholds  610  and  620 . In this instance, only the higher threshold (i.e., threshold  610 ) is considered. If the signal peak does not cross any threshold values, the next signal peak is selected at step  840  and process  800  continues until there are no more signal peaks. 
     If it is determined that the signal peak crosses a threshold value, at step  850  a portion of the signal surrounding the signal peak may be selected. For example, signal peak  511  ( FIG. 5 ) of respiration signal  505  exceeds the value of signal peak threshold  510 . As described above, the signal segment defined by the zero crossing before and after signal peak  511 , i.e., points  511   b  and  511   c , may be selected. Alternatively, the signal segment defined by the threshold crossing before and after signal peak  511 , i.e., points  511   d  and  511   e , may be selected. Any other suitable portion of the signal between the selected signal peak and adjacent signal peaks may also be selected. At step  860  the selected portion of the signal may be adjusted using linear or nonlinear scaling techniques, as described above. Finally, the next signal peak is selected at step  840  and process  800  continues until there are no more signal peaks. 
       FIG. 9  depicts an additional illustrative process for generating a normalized respiration signal from a scalogram  910 . Scalogram  910  of the wavelet transform may be generated or otherwise obtained at least in part from a received PPG signal using, for example a processor such as processor  412  ( FIG. 4 ) or microprocessor  48  ( FIG. 2 ). Scalogram  910  includes wavelet phase information from a received PPG signal in the region of the feature scales in wavelet space. Similar to the respiration ridge within respiration band B in the scalogram illustrated  FIG. 3(   c ) and the respiration ridge within a secondary bands C and D in  FIG. 3(   d ), which represent amplitude and/or scale modulation relating to respiration features as a function of time, ridge location  920  includes local phase values relating to respiration features as a function of time. A sinusoidal function indicative of respiration phase and having normalized height values may be generated from these local phase values by taking the sine or cosine of these values. Plot  930  is an illustrative cosine signal of wavelet phase values along ridge location  920 . Alternatively, an inverse wavelet transform may be performed on the local transform phase values along ridge location  920  to generate a normalized respiration signal. 
     It will also be understood that the above method may be implemented using any human-readable or machine-readable instructions on any suitable system or apparatus, such as those described herein. 
     The foregoing is merely illustrative of the principles of this disclosure and various modifications may be made by those skilled in the art without departing from the scope and spirit of the disclosure. The following claims may also describe various aspects of this disclosure.