CYSTUYARAYA
`
`US 20090105556A1
`
`as) United States
`a2) Patent Application Publication (io) Pub. No.: US 2009/0105556 Al
`Fricke etal.
`(43) Pub. Date:
`Apr. 23, 2009
`
`(54) MEASUREMENTOF PHYSIOLOGICAL
`SIGNALS
`
`(75)
`
`Inventors:
`
`.
`John Robert Fricke, Lexington,
`MA(US): Matthew Corbin
`Wiggins, Concord, MA (US)
`
`Correspondence Address:
`OCCHIUTI ROHLICEK & TSAO, LLP
`10 FAWCETT STREET
`CAMBRIDGE, MA 02138 (US)
`
`(73) Assignee:
`
`Tiax LLC, Cambridge, MA (US)
`
`(21) Appl. No.:
`
`12/240,651
`
`(22)
`
`Filed:
`
`Sep. 29, 2008
`
`Related U.S. Application Data
`
`(60) Provisional application No. 60/995,723, filed on Sep.
`28, 2007.
`
`Publication Classification
`
`(51)
`
`Int. Cl.
`(2006.01)
`AGIB 5/00
`(2006.01)
`AGIB 5/1455
`(52) US. CN. coeececcccsessssesessssssssseeeessen 600/301; 600/310
`(57)
`ABSTRACT
`
`A systemincludes an optical sensor and a signal processing
`module. The optical sensoris configured to be positioned on
`anarea of skin ofa patient. The optical sensor includesa light
`source for illuminating a capillary bed in the area of skin and
`a photodetector. The photodetectoris configured to receive an
`optical signal from the capillary bed resulting fromthe illu-
`mination and to convert the optical signal into an electrical
`signal, the optical signal characterizing a fluctuationinalevel
`of bloodinthe capillary bed. The signal processing moduleis
`configured to process the electric signal using a nonstationary
`frequency estimation method to obtain a processed signal
`related toat least one of a heart rate and a respirationrate of
`the patient. Another aspect relates to obtaining a quantity
`related to the blood pressure ofthe patient in addition to or
`instead of obtaining a processed signal related to at least one
`of the heart rate and the respirationrate ofthe patient.
`
`
`120 114
`
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`110
` 116
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`aa
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`001
`
`AppleInc.
`APLI1016
`U.S. Patent No. 8,923,941
`
`Apple Inc.
`APL1016
`U.S. Patent No. 8,923,941
`
`001
`
`

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`US 2009/0105556 Al
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`Apr. 23, 2009
`
`MEASUREMENT OF PHYSIOLOGICAL
`SIGNALS
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`
`[0001] This application claims priority to U.S. provisional
`application No. 60/995,723, filed Sep. 28, 2007, entitled
`“Method and Devices for Measurement of Multi-modal
`Physiological Signals,” which is incorporated herein by ref-
`erence,
`
`STATEMENT REGARDING FEDERALLY
`SPONSORED RESEARCH
`
`[0002] The subject matter described in this application was
`partially funded by the Government of the United States
`under Contract No, W917LK-04-P-0239 awarded by the
`U.S. Department of the Army. The governmenthas certain
`rights in the invention.
`
`FIELD OF THE INVENTION
`
`[0003] The inventionrelates to measurementofphysiologi-
`cal signals.
`
`BACKGROUND
`
`Physiological signals are important for monitoring a
`[0004]
`subject’s physical and cognitive state. Often, heart rate
`parameters are measured directly via electrocardiogram
`(ECG) measurements of a heart beat. Respiration rate data
`can be obtained froma respiration chest strap. Physiological
`signals can also be extracted from infrared (IR) photoplethys-
`mographs (PPG). The signals of interest include heart rate,
`respiration rate, continuous blood pressure, and intrathoracic
`pressure. With respect to blood pressure, there is technology
`related to collecting data at two locations on the body and
`using pulse transit time and other parameters as the basis of
`the pressure estimate.
`
`SUMMARY
`
`In a general aspect, a system includes an optical
`[0005]
`sensor and a signal processing module. ‘The optical sensoris
`configured to be positionedon anarea ofskin ofa patient. The
`optical sensor includesa light source for illuminating a cap-
`illary bed in the area ofskin and a photodetector. The photo-
`detector is configured to receive an optical signal from the
`capillary bed resulting from the illumination and to convert
`the optical signal into anelectrical signal, the optical signal
`characterizing a fluctuationin a level of blood in the capillary
`bed. The signal processing module is configured to process
`the electric signal using a nonstationary frequency estimation
`method to obtain a processed signal related to at least one of
`a heart rate and a respirationrate of the patient.
`[0006] Embodiments may include one or moreofthe fol-
`lowing. The system includes an output for providing infor-
`mation determined from the processed signal. The nonsta-
`tionary frequency estimation method includes a Hilbert
`transform method or an instantaneous frequency estimation
`method. The processed signal includes at least one ofinstan-
`taneous heart rate, inter-beat interval, heart rate variability,
`high-lowheart rate ratios, respiration rate, inter-breathinter-
`val, and respiration rate variability. The fluctuationin the level
`ofblood in the capillary bed relates to a change in atleast one
`
`ofvolumeand pressure ofthe thoracic cavity or to a change in
`at least one of volume and pressure ofan organ inthe thoracic
`cavity.
`[0007] The system includes an auxiliary sensor configured
`to detect an ambient signal. The auxiliary sensor includes at
`least one ofaccelerometer, a pressure sensor, an optical detec-
`tor, a temperature sensor, and a piezoelectric device. The
`signal processing module is configured to removeaneffect of
`the ambient signal from the electrical signal. The optical
`signal is a reflectance or a transmittanceof the capillary bed.
`[0008]
`Inanother general aspect, a method includes illumi-
`nating a capillary bedin anarea ofskin ofa patient, receiving
`an optical signal from the capillary bed resulting from the
`illumination, converting the optical signal into anelectrical
`signal, and processing the electrical signal using a nonstation-
`ary frequency estimation method to obtain a processedsignal
`related to at least one of a heart rate and a respiration rate of
`the patient. The optical signal characterizes a fluctuation in a
`level of blood in the capillary bed.
`[0009] Embodiments may include one or moreof the fol-
`lowing. The method includes outputting information deter-
`mined from the processed signal. Processing the electrical
`signal using the nonstationary frequency estimation method
`includes performing a Hilbert transform or processing the
`electrical signal using an instantaneous frequency estimation
`method. Processing the electrical signal using the instanta-
`neous frequency method includes bandpass filtering the elec-
`trical signal, determining an instantaneous frequency of the
`electrical signal, and using the instantaneous frequency to
`obtain the processed signal.
`[0010] The method further includes processing the electri-
`cal signal using a model to obtain a blood pressure signal
`related to a blood pressure of the patient. The optical signal
`characterizes a capillary refill time in the capillary bed. Pro-
`cessingthe electrical signal includes processingthe electrical
`signal in real time.
`[0011]
`In another aspect, a method for monitoring blood
`pressure includes illuminating a capillary bed in an area of
`skin of a patient, receiving anoptical signal fromthe capillary
`bed resulting from the illumination, converting the optical
`signal into an electrical signal, and processing the electrical
`signal using a model characterizing a relationship of the fluc-
`tuation in the level of blood and the blood pressure of the
`patient to obtain a quantity related to the blood pressure of the
`patient. The optical signal characterizes a fluctuation in a
`level of bloodin the capillary bed of the patient.
`[0012] Embodiments may include one or moreof the fol-
`lowing. The method includes outputting information deter-
`mined based on the quantity related to the blood pressure of
`the patient. The optical signal characterizes a capillary refill
`time. The method further includes engaging a device to
`restrict circulation in the capillary bed of the patient and
`disengaging the device prior to receiving the optical signal
`fromthe capillary bed. The disengaging ofthe device occurs
`gradually. The device is an active clamping device.
`[0013] The quantity related to the blood pressure of the
`patient is a quantity related to the continuous blood pressure
`ofthe patient. Applying the modelincludes applying a model
`including circuit elements or properties ofthe capillary bed.
`The method further includes calibrating the model on the
`basis of a blood pressure of the patient determined by using a
`blood pressure cuff.
`
`022
`
`022
`
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`Apr. 23, 2009
`
`[0014] Embodiments may include one or more ofthe fol-
`lowing advantages.
`[0015] A system or method as described above can be used
`for both military and civilian applications. Combat casualty
`care requires close monitoringof vital signs from the moment
`that a medic first attends to a wounded soldier in the battle-
`field and thence through the many transfer stages to the point
`offull hospital care, generally removed from the combat
`scene. Similar needs are evident in the civilian community
`wherecritical care is administered by first responders at the
`scene ofaccidents, by emergency room staff, and by intensive
`care unit staff. It is often desirable to obtain maximuminfor-
`mation using as little equipment as possible. The system and
`method described herein support this need. They reduce the
`burdenof equipmentlogistics, the burden of extra wires and
`sensors on and around the patient, and the complexity and
`cost of using multiple devices.
`[0016]
`For both military and civilian applications, a dispos-
`able, wearable device in keeping with the system and method
`described herein can be adapted to stay with a patient and to
`report vital signs throughout the care and transport processes.
`Further, the system can be configured to provide medical
`personnel with real-time visibility of vital signs as well as
`recording ofthis informationfor playback by attending medi-
`cal staffat a later time. The disposability ofthe device allows
`it to be fabricated with low cost parts and eliminates the need
`for sanitization and asset tracking logistics in large scale
`clinical or military uses.
`[0017]
`Such system and methods additionally support
`applications in fitness monitoring, wheretheir ease ofuse and
`robustness make them a compelling alternative to chest strap
`monitors for the monitoring ofcardiac and respiratory param-
`eters during exercise. An ear-worndevice canalso integrate a
`speaker unit for mobile electronic devices such as mobile
`phones or music players.
`[0018] An advantage of applying a nonstationary fre-
`quency estimation method (e.g., analysis involving monitor-
`ing the frequency changes of the signal over time, such as
`monitoring changesin the instantaneousprincipal frequency
`overtime) is that it is possible to avoid a tradeoff inherentin
`manystationary estimation methods betweenfrequencyreso-
`lution and duration of data signals being analyzed. For
`example,ifthe signal is assumedto be stationary within each
`ofa series of data windows, the frequency resolutionis gen-
`erally inversely proportional to the duration of the window.
`As the window durationincreases, the assumptionofa sta-
`tionary signal is increasingly violated and/or nonstationary
`events (e.g., transients) are more difficult to detect. At least
`some nonstationary frequency analysis methods, which may
`be based, without limitation, ona Hilbert transform approach,
`tracking of a nonstationary model, nonstationary principal
`frequency analysis, or other time-frequency methods, miti-
`gate the effects of such a time-frequency tradeoff. Purther-
`more, use of such nonstationary techniques, as opposed to use
`of time domain peak picking and/or threshold based tech-
`niques, can provide robustness ofalgorithm against artifacts,
`and provide sensitivity to periodicity without being burdened
`by a window that can reduce the time resolution.
`[0019] Other features and advantages are apparent fromthe
`following description and from the appended claims.
`
`BRIEF DESCRIPTION OF DRAWINGS
`
`FIG. 1is.aschematic diagram ofa photoplethysmo-
`[0020]
`graph (PPG) sensor system.
`
`[0021] FIG.2isa graph of a PPG detector signal taken over
`a 25 second period by an earlobe PPG device.
`[0022]
`FIG. 3 is a flow diagramofsignal processing of a
`detector signal from a PPG device to obtain heart rate and
`respiration rate parameters.
`[0023]
`FIG. 4isagraph ofa result of band-passfiltering the
`data shown in FIG, 2 between 0.5 Hz and 5.5 Hz to extract a
`cardiac signal.
`[0024]
`FIG. 5isagraph ofa result of band-passfiltering the
`data shownin FIG. 2 between 0.17 Hz and 0.5 Hz to extract a
`respiration signal.
`[0025]
`FIG. 6isagraph ofaninter-beat interval obtained by
`applying an instantaneous frequency method to the cardiac
`signal shownin FIG, 4,
`[0026]
`FIG. 7 is a graph ofa spectral analysis ofthe inter-
`beat interval data shown in FIG. 6.
`
`FIG. 8 isa graphofthe respiration rate obtained by
`[0027]
`applying an instantaneous frequency method to the respira-
`tion signal shownin FIG. 5.
`[0028]
`FIG. 9 is adiagram of PPG measurements related to
`physiological states used to determineintrathoracic pressure.
`[0029]
`FIG. 10 is a graphof the output ofa matched filter-
`ing process using the PPG detectorsignal shownin FIG. 2 and
`a pulse pilotsignal.
`[0030]
`FIG. 11 is a block diagramofa least mean squares
`(LMS) adaptive filter.
`[0031]
`FIG. 12 is a schematic diagram ofan active clamp-
`ing mechanismused to stimulate capillary refill.
`[0032]
`FIG. 13 is a diagram ofa system modelrelating a
`PPG signal to blood pressure.
`[0033]
`FIG. 14 is a graphof trends in various physiological
`parameters before and during a stress event.
`[0034]
`FIG. 15 is a block diagram ofa portable electronics
`unit.
`
`FIG. 16 is a flow diagram of methodsto estimate a
`[0035]
`heart rate and a respirationrate.
`[0036]
`FIG. 17 is a flow diagram of a processing delay in
`the estimationofa heart rate.
`[0037]
`FIG. 18 is a flow diagram of a processing delay ina
`first method for the estimation of a respirationrate.
`[0038]
`FIG. 19 is a flow diagram of a processing delay ina
`second method for the estimation ofa respiration rate.
`[0039]
`FIG. 20 is a flow diagram ofa processing delay ina
`third method for the estimation of a respiration rate.
`
`DETAILED DESCRIPTION
`
`[0040] Referring to FIG. 1, examples of an infrared pho-
`toplethysmograph (PPG) device 100 are used to obtain physi-
`ological signals related to one or more of heart rate, respira-
`tion rate, blood pressure, and intrathoracic pressure. Such
`signals may be relevant
`for monitoring a person’s state,
`including one or more ofthe person’s physical state, long-
`term health, psychological state, and/or cognitive state. More
`generally, the physiological signals may provide information
`about the activity of the person’s sympathetic and parasym-
`pathetic nervous system. The PPGdevice 100 illustrated in
`FIG. 1 is attached to an earlobe 102 of a person, for example,
`using a clamping or adhesive approach. However, in other
`embodiments, PPG device 100 is used onother areas of the
`skin of a person, including but not limited to a portion of a
`forehead, a neck, an arm, a forearm,a finger, a leg, a back, an
`abdomen, or a stomach. In general, a requirement for the
`positioning of PPG device 100 is that the PPG sensor be
`located suchthat it can obtain a measurementvia the skin that
`
`023
`
`023
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`US 2009/0105556 Al
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`Apr. 23, 2009
`
`is related to bloodflow or pressure, for example to measure a
`level of blood in a capillary bed 104, for example, a blood
`volume, a rate of blood flow, or a rate of change of blood
`volume. Note also that the approachis not limited to use of a
`single PPGdevice on anindividual. In some embodiments,
`multiple PPG devices are used, for example, on the torso
`and/or at different extremities, and signals obtained at the
`different PPG devices are processed independently or incom-
`bination to determine underlying characteristics of the indi-
`vidual’s state.
`
`Insome embodiments, such as that shownin FIG. 1,
`[0041]
`an infrared light source 106 illuminates the earlobe 102. The
`blood level in capillary bed 104 affects the amountoflight
`108 that is backscattered or reflected by earlobe 102. Light
`108 backscattered by earlobe 102 is received by an optical
`transducer such as a photodetector 110 and converted into a
`detector signal 112. Since the blood flowin capillary bed 104
`is controlled by the heart beatofthe person and thus the blood
`level in the capillary bed varies with time, the backscattered
`light 108 and hence the detector signal 112 are also time-
`varying. In another embodiment, the PPG sensor operates in
`transmission modeandthelight transmitted throughthe cap-
`illary bed is received by the photodetector.
`[0042] Thedetector signal 112 is sent to a signal processing
`unit 114 which processes the detector signal, which contains
`informationaboutthe person’spulse, to extract desired physi-
`ological data, in various embodiments including one or more
`ofinstantaneousheart rate, inter-beat interval, heart rate vari-
`ability, high-low heart rate ratio, respirationrate, inter-breath
`interval, respiration rate variability, blood pressure, and
`intrathoracic pressure. A single PPG device 100, referred to
`belowas an Integrated Multi-Modal Physiological Sensor
`(IMMPS), is capable of producing multiple (or all) of such
`types of physiological data.
`[0043]
`Insome embodiments, the PPG device 100 provides
`real-time visibility of physiological parameters and vital
`signs, which can be transmitted to other equipment forreal-
`time processing or for playback or off-line processing at a
`later time. In some embodiments, the PPG device includes
`user output devices, such as a set oflight emitting diodes
`(LEDs) (e.g., a red LED 116, a yellow LED 118, and a green
`LED 120) or an audio device for producing alert sounds,
`which provide on-device status on PPG device 100. As an
`example for use of such output devices, when a selected
`physiological parameteris in a normal range, green LED 120
`is turned on; whenthe physiological parameter is in a slightly
`abnormal range, yellow LED 118 is turned on; whenthe
`physiological parameteris in a dangerous range, red LED 116
`is turned on. In some embodiments, the audio output deviceis
`used to provide other audio output, such as the output for an
`electronic device such as a mobile phone ora musicplayer. In
`some embodiments, a wireless link 122 to an external moni-
`toring system 124, such as a bedside system or a wearable
`system, provides sensordata to the external system enabling
`a numeric readout 126 of various physiological parameters.
`In some embodiments, the PPG device, or at least some
`wearable portion ofthe device, is disposable. In such dispos-
`able embodiments, the bedside system can be designed to be
`sterilized and reused: in another embodiment, the bedside
`systemitself is also disposable. In some embodiments, the
`bedside system includes or communicates with a centralized
`monitoring system that monitors PPG devices of multiple
`patients.
`
`the photodetector based
`In some embodiments,
`[0044]
`detector signal is augmented with other signals, for example,
`accelerometer or pressure sensor signals. For example, aux-
`iliary sensors 130 are connected tosignal processing unit 114
`via a wired connection 132. In other embodiments, auxiliary
`sensors 130 are connected to signal processing unit 114 viaa
`wireless connection. Auxiliary sensors 130, such as tempera-
`ture sensors, accelerometers, pressure transducers, optical
`detectors, or piezoelectric films or matrices can provide aux-
`iliary signals 132 related to ambient sources of noise to signal
`processing unit 114. Signal processing unit 114 incorporates
`auxiliary signals 132 into the signal processing, for example,
`to increase the signal-to-noise ratio ofthe desired physiologi-
`cal data.
`
`Heart and Respiration Rate Signals
`
`[0045] Referring to FIG. 2, in an embodiment of the PPG
`device that uses a photodetector signal obtained from at an
`earlobe location, a detector signal 200 obtained from the PPG
`device 100 has a high-frequency pulse signal 202 whose local
`peaks in the time domain have a one-to-one correspondence
`with cardiac beats. Significant low-frequency amplitude vari-
`ability in the detector signal is due in large part a respiration
`signal 204, which modulates the baseline of the pulse signal.
`[0046] The time varying heart andrespiration components
`in detector signal 200 can be modeled as
`S(Q)=A(feos [MAHPAT)|+Ap(theos [Mpt4h,_( T)]+
`Nit),
`
`qd)
`
`where A,,{t) is the amplitude modulationofpulse signal 202,
`,,t) is the frequency modulation of pulse signal 202, p;,(t) is
`the phase modulation ofpulse signal 202, A,(t) is the ampli-
`tude modulation ofrespiration signal 204, m,(t) is the fre-
`quency modulation of respiration signal 204, ,(t) is the
`phase modulation of respiration signal 204, and N(t) ts the
`time varying noise, which includes baseline drift and broad-
`bandnoise in the overall signal band.
`[0047] Given the measured detector signal 200 (s(t), signal
`processing is performed to estimate the slowly varying com-
`ponents of the heart rate «,,(t) and the respiration rate «,(t).
`It is knownthat ,,(t)=0,,.>~1 beat per second | Hz for heart
`rate and w,(t)=,,=12 breaths per minute=0.2 Hz for respi-
`ration rate.
`
`[0048] Amplitude, phase, and frequency modulation cause
`spectral spread that broadens the pure tones implied by these
`frequencies. Amplitude and phase modulationand rapid fluc-
`tuations of the frequency modulation are confounding com-
`ponents ofdetector signal 200. The slowly varying compo-
`nents of @(t) are the desired components for obtaining heart
`and respirationrate information.
`is com-
`[0049]
`For both heart and respiration rate, w(t),
`posed of three parts: constant frequency ,, which is the
`nominalheart or respiration rate: a zero-mean, slowly varying
`frequency component 2, having a time scale of minutes; and
`a zero-mean.rapidly varying frequency component Q,having
`atimescale ofseconds.In this case, the composite heart rate
`or respiration rate is written as
`
`a(t) 0,42,(1)+0240).
`
`(2)
`
`The signal of interest is the combinationofthe constant and
`the slowly varying component(for both heart rate and respi-
`ration rate) and is written as
`
`o(e)=0,+2,(0).
`
`G)
`
`024
`
`024
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`US 2009/0105556 Al
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`Apr. 23, 2009
`
`The phase modulation noted is Eq. (1), p(t), is assumed to be
`small, since large phase modulation can be represented as
`frequency modulation andthisis already captured in 2, or Q,
`[0050] Applying Eq. (3) to Eq. (1), a new equation for the
`measured raw signal 200 is obtained:
`S(t)=Az,(t)cos [OptD+a(feos [
`Mpl(O+Pp(O]+N(0),
`
`(4)
`
`where for both heart and respiration rate, small components
`,(t) are defined as
`O.4t)= |lrde+pi(r)
`
`(5)
`
`and by construction |@,(t)l<<1 and @,(t) is zero mean.
`[0051] Using the Lawof Cosines and the fact that |p,(t)
`|<<1, the following equation for raw signal 200 is obtained:
`SQAAOL cos [Op(0)PerelOsin [OANt}+Ag(O{
`cos [Mlt)t/-p,p(fsin [Mp(t)t]/}+N().
`
`(6)
`
`then true beat peaks may be missed, For general processing it
`is convenient to select a single threshold, but if the data are
`sufficiently variable then selecting a single threshold is not
`possible.
`[0055] Other approaches to processing the cardiac signal
`use nonstationary frequency estimation methods. For
`instance, instantaneous frequency computation component
`306, 318 are used to determine the time-varying principal
`frequencies present in bandpass filtered signals.Approaches
`to instantaneous frequency computation include Hilbert
`Transform methods, which areparticularly effective because
`the band-pass filtered cardiac signal shown in FIG. 4 has a
`strong sinusoidal content and because systematic changes in
`the IBI over long periods oftimeare oftenofinterest. Model-
`based approaches, such as Kalman filtering approaches
`described later in this document can also be used, with state
`variables (or alternatively time-varying system parameters)
`that are estimated corresponding to the instantaneous fre-
`[0052] The formulation in Eq. (6) of PPG detector signal
`quencies ofinterest. Yet other approaches to tracking instan-
`200 suggests a number of methods to estimate the desired
`taneous frequency can be based on adaptive modeling of the
`slowly varying heart and respiration rate signals @,,(t) and
`underlying quasi-periodic heart signal.
`«,(t), respectively. Such estimation techniques can include
`[0056]
`In some embodiments, an approach to determining
`instantaneous frequency determination via analytic signals,
`the instantaneous frequency relies on analytic signals, which
`moving averages, band passfiltering, synchronous detection,
`are signals that have no negative frequency components.
`correlation detection, narrowband processes (e.g., demodu-
`Based onthe properties ofthe Fouriertransform, a signal with
`lation), matched filtering, wavelet filtering, short-time fre-
`no negative frequencies is a complex signal
`in the time
`quency analysis (e.g., short-time fast Fourier transform,
`domain. Givenareal signal, x,(t), the corresponding analytic
`Wigner-Ville transform), state estimation (e.g., Kalmanfil-
`signal, x,,(t)=x,(t)+jx,(t), has the same positive frequency
`tering, unscented filtering), Doppler processing, or a combi-
`spectrum as x,(t) but has zero negative frequency values.
`nation of the above methods. A numberofthese techniques
`Thus, the imaginary signal x,(t) must be determined. The
`can be implemented to accountforthe nonstationary nature of
`utility of computing the analytic signal becomes apparent
`the detector signal, which relates to the time variation of the
`whenit is written as follows:
`frequency modulationsignals, w(t).
`[0053] Referring to FIG. 3, one example of a procedure for
`obtaining heart rate parameters and/or respiration rate param-
`eters involves receiving the detector signal 200, such as that
`shownin FIG, 2, from a PPG photodetector (IR Plethysmo-
`graph 300). To emphasize the pulse signal in order to extract
`cardiac parameters from the detector signal, the respiratory
`modulationis removed by band-passfiltering (302) the detec-
`tor signal between approximately 0.5 Hz and approximately
`5.5 Hz. Band-pass filtering of the detector signal shownin
`FIG. 2 results ina cardiac signal shown in FIG. 4, which has
`significantly less amplitude variability due to respiratory con-
`tamination. The band-passfiltered signal pulse signal can be
`expressed as
`
`X(t) = x) + prio
`
`= Are",
`
`(8)
`
`where A(t) is the time varying magnitude of the complex
`signal, i.e., the envelope, and (t) is the time varying instan-
`taneous phase of the complex signal. By construction, the
`magnitude and instantaneous phase can be written as:
`A(t= beOO and
`
`p(r)=tan” !(x,(t)/x,(2)) .
`
`(9)
`
`HORAMOL cos [Oy(Ot/-OyAdsin