Biological information detection device and biological information detection method

The biological information detection device improves measurement accuracy by generating a mutual relation function to isolate noise components from radar signals, enabling precise respiratory and heart rate frequency detection.

WO2025022745A1PCT designated stage expired Publication Date: 2025-01-30MURATA MFG CO LTD
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Patent Information

Application Number
PCT/JP2024/015816
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-07-21
Filing Date
2024-04-23
Publication Date
2025-01-30

AI Technical Summary

Technical Problem

Existing biological information detection systems face reduced measurement accuracy due to noise components in the I, Q, and phase or amplitude changes of radar signals, which affects the precision of respiratory and heart rate cycle measurements.

Method used

A biological information detection device and method that generates a mutual relation function between the time change of the radar signal phase and amplitude, using noise components to derive high-precision respiratory and heart rate frequencies by separating and removing noise components from the radar signal, thereby improving measurement accuracy.

Benefits of technology

The solution enhances the accuracy of acquiring biological information by isolating noise components and extracting high-precision respiratory and heart rate frequencies, leading to improved detection precision.

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Abstract

The present invention achieves a biological information detection device and a biological information detection method that make it possible to appropriately distinguish an observation object and a non-observation object. This biological information detection device comprises: a radar (11) that emits a transmission wave (Tx) to an object for which biological information is acquired, receives a reflected wave (Rx) of the transmission wave (Tx), and thus acquires a radar signal; a cross-correlation function generation unit (12) that generates a cross-correlation function between temporal change in the phase of the radar signal and temporal change in the amplitude; and a respiration calculation unit (13) that derives, on the basis of the cross-correlation function, the respiration frequency of the object for which biological information is acquired.
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Description

Biological information detection device and biological information detection method

[0001] The present invention relates to a biological information detection device and a biological information detection method.

[0002] Systems that use radar (RADAR: Radio Detection And Ranging) to detect a human body and acquire biometric information based on the body surface displacement are being introduced. Radar systems analyze the reflected waves of radio waves emitted from an antenna to identify targets and acquire biometric information.

[0003] Patent Document 1 discloses a respiratory cycle measuring device that measures the respiratory cycle using the results of autocorrelation processing of time-series changes in the I component, Q component, phase, or amplitude of a radar signal. Patent Document 2 discloses a cardiac cycle measuring device that measures the cardiac cycle using the results of autocorrelation processing of time-series changes in the I component, Q component, phase, or amplitude of a radar signal.

[0004] Furthermore, Patent Document 3 discloses a sensor device and sensing method for sensing a living body using an FMCW radar. This patent document 3 states that the phase information obtained by analyzing an IF signal obtained by mixing the transmitted and received waves of the FMCW radar is time-differentiated to separate the heartbeat component from the respiratory component and body movement component, and that the respiratory component and body movement component are further time-differentiated twice to essentially cancel out the heartbeat component, leaving only the heartbeat component.

[0005] JP 2020-092782 A JP 2020-092783 A JP 2021-001735 A

[0006] In Patent Documents 1 and 2, if the I component, Q component, phase, or amplitude of the radar signal contains noise components, the measurement accuracy of the respiratory cycle or cardiac cycle may be reduced. In Patent Document 3, high-frequency noise components contained in the phase information are emphasized by time differentiation, which may reduce the accuracy of acquiring the cardiac component.

[0007] The present disclosure has been made in view of the above, and aims to provide a biological information detection device and a biological information detection method that can improve the accuracy of acquiring biological information.

[0008] A bioinformation detection device according to one aspect of the present disclosure includes a radar that emits a transmission wave to a subject from which bioinformation is to be obtained and receives a reflected wave of the transmission wave to obtain a radar signal, a cross-correlation function generation unit that generates a cross-correlation function between a time change in the phase of the radar signal and a time change in the amplitude of the radar signal, and a respiration calculation unit that derives a respiration frequency of the subject from which bioinformation is to be obtained based on the cross-correlation function.

[0009] This configuration allows highly accurate acquisition of respiratory frequency using a cross-correlation function that removes both noise components contained in the time-varying phase of the radar signal and noise components contained in the time-varying amplitude of the radar signal, thereby improving the accuracy of acquiring biological information.

[0010] A biometric information detection method according to one aspect of the present disclosure includes the steps of generating a cross-correlation function between a time change in the phase of a radar signal acquired by a radar and a time change in the amplitude of the radar signal, and deriving a respiratory frequency of a subject from which biometric information is to be acquired based on the cross-correlation function.

[0011] This configuration allows highly accurate acquisition of respiratory frequency using a cross-correlation function that removes both noise components contained in the time-varying phase of the radar signal and noise components contained in the time-varying amplitude of the radar signal, thereby improving the accuracy of acquiring biological information.

[0012] According to the present disclosure, it is possible to realize a biological information detection device and a biological information detection method that can improve the accuracy of acquiring biological information.

[0013] FIG. 1 is a block diagram showing a schematic configuration of a biometric information detection device according to an embodiment. FIG. 2 is a conceptual diagram showing the positional relationship between a radar and a biometric information acquisition target. FIG. 3 is a diagram showing an example of a time-domain signal indicating a time change in the phase of a radar signal. FIG. 4 is a diagram showing an example of a time-domain signal indicating a time change in the amplitude of a radar signal. FIG. 5 is a Fourier spectrum of the time-domain signal shown in FIG. 3. FIG. 6 is a Fourier spectrum of the time-domain signal shown in FIG. 4. FIG. 7 is a flowchart showing an example of a biometric information acquisition process in a biometric information detection device according to an embodiment. FIG. 8 is a diagram showing an example of a time-domain signal indicating a cross-correlation function according to an embodiment. FIG. 9 is a Fourier spectrum of the time-domain signal shown in FIG. 8. FIG. 10 is a diagram showing an example of a time-domain signal indicating a second derivative of a cross-correlation function according to an embodiment. FIG. 11A is a diagram showing a first example of a first curve fitting process. FIG. 11B is a diagram showing a second example of the first curve fitting process. FIG. 12A is a diagram showing a first example of a third curve fitting process. FIG. 12B is a diagram showing a second example of the third curve fitting process.

[0014] Hereinafter, biological information detection devices and biological information detection methods according to embodiments will be described in detail with reference to the drawings. However, the present disclosure is not limited to these embodiments.

[0015] 1 is a block diagram showing a schematic configuration of a biological information detection device according to an embodiment. The biological information detection device 1 according to the embodiment includes a radar 11, a cross-correlation function generator 12, a respiration calculator 13, a differentiation unit 14, and a heart rate calculator 15.

[0016] The radar 11 emits a transmission wave Tx, for example, in the millimeter wave band or microwave band, toward a target from which biological information is to be acquired in the biological information detection device according to the embodiment, and receives a reflected wave Rx of the transmission wave Tx. Examples of the radar 11 include an FMCW (Frequency Modulated Continuous Wave) radar, a Doppler radar, an UWB (Ultra Wide Band) radar, and a pulse radar.

[0017] 2 is a conceptual diagram showing the positional relationship between the radar and the biometric information acquisition target. The time change φ(t) in the phase of the body surface displacement component of the biometric information acquisition target included in the signal acquired by the radar 11 (hereinafter also referred to as "radar signal") is expressed by the following equation (1). Furthermore, the time change A(t) in the amplitude of the body surface displacement component of the biometric information acquisition target included in the radar signal is expressed by the following equation (2). In the following equations (1) and (2), R represents the distance between the radar 11 and the biometric information acquisition target, d(t) represents the body surface displacement of the biometric information acquisition target, and λ represents the wavelength of the radar signal. A in equation (2) 0 is a predetermined constant value.

[0018]

[0019]

[0020] Here, when the above equation (2) is expanded by Taylor assuming that R<<d(t), the following equation (3) is obtained.

[0021]

[0022] From the above equations (1) and (3), the time change φ(t) in the phase of the body surface displacement component of the biological information acquisition subject included in the radar signal and the time change A(t) in the amplitude of the body surface displacement component of the biological information acquisition subject included in the radar signal are each proportional to the body surface displacement d(t) of the biological information acquisition subject. In other words, the time change in the phase of the radar signal and the time change in the amplitude of the radar signal are correlated.

[0023] 3 is a diagram showing an example of a time domain signal indicating a time change in the phase of a radar signal, where the vertical axis represents the time change φ′(t) of the phase of the radar signal.

[0024] 4 is a diagram showing an example of a time domain signal indicating the time change in amplitude of a radar signal, where the vertical axis represents the time change A'(t) of the amplitude of the radar signal.

[0025] Fig. 5 is a Fourier spectrum of the time-domain signal shown in Fig. 3. Fig. 5 illustrates a frequency-domain signal obtained by Fourier transform processing of the time-domain signal shown in Fig. 3. The vertical axis of Fig. 5 represents the signal value sigφ' of the frequency-domain signal.

[0026] Fig. 6 is a Fourier spectrum of the time-domain signal shown in Fig. 4. Fig. 6 illustrates a frequency-domain signal obtained by Fourier transform processing of the time-domain signal shown in Fig. 4. The vertical axis of Fig. 6 represents the signal value sigA' of the frequency-domain signal.

[0027] The frequency fr component shown in Figures 5 and 6 indicates a displacement component due to respiration of the subject of biometric information acquisition. The frequency fh component shown in Figures 5 and 6 indicates a displacement component due to the heartbeat of the subject of biometric information acquisition. The heartbeat displacement component is extremely small compared to the respiration displacement component. Therefore, in the examples shown in Figures 5 and 6, the heartbeat displacement component is not observed as a peak value. Specifically, for example, by differentiating the radar signal twice, low-frequency components such as the respiration displacement component are canceled, making it possible to acquire the heartbeat displacement component.

[0028] Here, the reflected wave Rx received by the radar 11 contains noise components. Therefore, the radar signal also contains noise components contained in the reflected wave Rx. Furthermore, the noise components contained in the time change φ'(t) in the phase of the radar signal and the noise components contained in the time change A'(t) in the amplitude of the radar signal have different frequency components.

[0029] A specific example of the biological information acquisition process in the biological information detection device 1 according to the present disclosure will be described below. Fig. 7 is a flowchart showing an example of the biological information acquisition process in the biological information detection device according to the embodiment.

[0030] In the biological information detection device 1 according to the present disclosure, the cross-correlation function generator 12 generates a cross-correlation function C(τ) between the time change φ′(t) in the phase of the radar signal and the time change A′(t) in the amplitude of the radar signal (cross-correlation function generation process, step S101). The cross-correlation function C(τ) is expressed by the following equation (4): In the following equation (4), T represents the signal length.

[0031]

[0032] 8 is a diagram illustrating an example of a time domain signal showing a cross-correlation function according to an embodiment, and FIG 9 is a Fourier spectrum of the time domain signal shown in FIG 8.

[0033] Specifically, the cross-correlation function generator 12 obtains the cross-correlation function C(τ) shown in Fig. 8 by, for example, performing an inverse Fourier transform on the product of the complex conjugate of the Fourier spectrum shown in Fig. 5 and the Fourier spectrum shown in Fig. 6. Alternatively, the cross-correlation function generator 12 obtains the cross-correlation function C(τ) shown in Fig. 8 by, for example, performing an inverse Fourier transform on the product of the Fourier spectrum shown in Fig. 5 and the complex conjugate of the Fourier spectrum shown in Fig. 6. This generates a cross-correlation function C(τ) from which both the noise components included in the time change φ'(t) in the phase of the radar signal and the noise components included in the time change A'(t) in the amplitude of the radar signal have been removed.

[0034] The differentiating unit 14 generates a second-order differential C"(τ) by differentiating the cross-correlation function C(τ) generated by the cross-correlation function generating unit 12 twice (differentiation process, step S102). Fig. 10 is a diagram showing an example of a time-domain signal indicating the second-order differential of the cross-correlation function according to the embodiment.

[0035] Here, if the displacement component due to breathing is dr(t) and the displacement component due to heartbeat is dh(t), the body surface displacement component d(t) of the subject of biological information acquisition can be expressed by the following equation (5).

[0036]

[0037] Further, the displacement component dr(t) due to respiration can be expressed by the mathematical model (first mathematical model) shown in the following equation (6). In the mathematical model shown in the following equation (6), the variable α 2indicates the fundamental frequency of the displacement component dr(t). 1 indicates the amplitude of the fundamental component of the displacement component dr(t), and the variable α 3 indicates the phase of the fundamental component of the displacement component dr(t). 4 indicates the amplitude of the second harmonic component of the displacement component dr(t), and the variable α 5 indicates the phase of the second harmonic component of the displacement component dr(t). 6 indicates the amplitude of the third harmonic component of the displacement component dr(t), and the variable α 7 indicates the phase of the third harmonic component of the displacement component dr(t).

[0038]

[0039] Further, the displacement component dh(t) due to the heartbeat can be expressed by the mathematical model (second mathematical model) shown in the following equation (7). In the mathematical model shown in the following equation (7), the variable α 9 indicates the fundamental frequency of the displacement component dh(t). 8 indicates the amplitude of the fundamental component of the displacement component dh(t), and the variable α 10 indicates the phase of the fundamental component of the displacement component dh(t). 11 indicates the amplitude of the second harmonic component of the displacement component dh(t), and the variable α 12 indicates the phase of the second harmonic component of the displacement component dh(t). 13 indicates the amplitude of the third harmonic component of the displacement component dh(t), and the variable α 14 indicates the phase of the third harmonic component of the displacement component dh(t).

[0040]

[0041] Although the present disclosure shows an example in which the modeling includes harmonic components up to the third harmonic of each displacement component, the modeling may also include harmonic components up to the fourth harmonic or higher of each displacement component, or may include harmonic components up to the second harmonic, or may include only the fundamental wave.

[0042] The respiration calculation unit 13 applies the displacement component dr(t) shown in the above equation (6) to the cross-correlation function C(τ) generated by the cross-correlation function generation unit 12, and calculates each variable α of the displacement component dr(t) shown in the above equation (6). 1 , α 2 , α 3 , α 4 , α 5 , α 6 , α 7 Specifically, the respiration calculation unit 13 performs a curve fitting process to fit the mathematical model shown in the above equation (6) to the cross-correlation function C(τ) generated by the cross-correlation function generation unit 12 using a curve fitting method (first curve fitting process, step S103).

[0043] Fig. 11A is a diagram showing a first example of the first curve fitting process. Fig. 11B is a diagram showing a second example of the first curve fitting process. Fig. 11A shows an example in which particle swarm optimization (PSO) is used as an example of the curve fitting method. Fig. 11B shows an example in which a genetic algorithm (GA) is used as an example of the curve fitting method.

[0044] The respiration calculation unit 13 calculates a variable α derived by a curve fitting method using particle swarm optimization (PSO) shown in FIG. 11A or a curve fitting method using a genetic algorithm (GA) shown in FIG. 11B. 2 Specifically, the respiratory frequency (variable α 2 ) is set to, for example, 0.33 Hz. The respiratory frequency (variable α 2 ) is set to, for example, 0.33 Hz.

[0045] The heart rate calculation unit 15 calculates the variable α derived by the respiration calculation unit 13 in step S103 for the displacement component dr(t) shown in the above equation (6).2 is applied to the second derivative C″(τ) of the cross-correlation function C(τ), and each variable α of the displacement component dr(t) shown in the above equation (6) is 1 , α 3 , α 4 , α 5 , α 6 , α 7 Specifically, the heart rate calculation unit 15 performs a curve fitting process to fit the mathematical model shown in the above equation (6) to the second derivative C″(τ) of the cross-correlation function C(τ) using a curve fitting technique (second curve fitting process, step S104).

[0046] Next, the heart rate calculation unit 15 calculates the variable α 2 , and each variable α of the displacement component dr(t) derived in step S104 1 , α 3 , α 4 , α 5 , α 6 , α 7 Furthermore, the displacement component dr(t) shown in the above equation (6) and the displacement component dh(t) shown in the above equation (7) are substituted into the above equation (5), and applied to the second-order differential C″(τ) of the cross-correlation function C(τ), and each variable α of the displacement component dh(t) shown in the above equation (7) is obtained. 8 , α 9 , α 10 , α 11 , α 12 , α 13 , α 14 Specifically, the heart rate calculation unit 15 performs a curve fitting process to fit the mathematical model shown in the above equation (5) to the second derivative C″(τ) of the cross-correlation function C(τ) using a curve fitting technique (third curve fitting process, step S105).

[0047] Fig. 12A is a diagram showing a first example of the third curve fitting process. Fig. 12B is a diagram showing a second example of the third curve fitting process. Fig. 12A shows an example in which particle swarm optimization (PSO) is used as an example of the curve fitting method. Fig. 12B shows an example in which a genetic algorithm (GA) is used as an example of the curve fitting method.

[0048] The heart rate calculation unit 15 calculates a variable α derived by a curve fitting method using particle swarm optimization (PSO) shown in FIG. 12A or a curve fitting method using a genetic algorithm (GA) shown in FIG. 12B. 9 Specifically, the heartbeat frequency (variable α 9 ) is set to, for example, 1.20 Hz. The heartbeat frequency (variable α 9 ) is set to, for example, 1.20 Hz.

[0049] The curve fitting methods (particle swarm optimization (PSO) and genetic algorithm (GA)) applied in the respiration calculation unit 13 and the heart rate calculation unit 15 are merely examples, and the present disclosure is not limited to the curve fitting methods.

[0050] The above-described biometric information acquisition process in the biometric information detection device 1 according to the present disclosure allows a highly accurate respiratory frequency to be acquired using a cross-correlation function C(τ) from which both the noise components contained in the time change φ'(t) in the phase of the radar signal and the noise components contained in the time change A'(t) in the amplitude of the radar signal have been removed. Furthermore, a highly accurate heartbeat frequency can be acquired using the second-order derivative C''(τ) of the cross-correlation function C(τ) from which low-frequency components, including displacement components due to respiration, have been removed. This improves the accuracy of biometric information acquisition.

[0051] The above-described embodiments are intended to facilitate understanding of the present disclosure and are not intended to limit the present disclosure. The present disclosure may be modified or improved without departing from the spirit thereof, and equivalents thereof are also included in the present disclosure.

[0052] The present disclosure can have the following configurations as described above or instead of the above.

[0053] (1) A biometric information detection device according to one aspect of the present disclosure includes a radar that emits a transmission wave to a subject from which biometric information is to be obtained and receives a reflected wave of the transmission wave to obtain a radar signal; a cross-correlation function generation unit that generates a cross-correlation function between a time change in the phase of the radar signal and a time change in the amplitude of the radar signal; and a respiration calculation unit that derives a respiration frequency of the subject from which biometric information is to be obtained based on the cross-correlation function.

[0054] In this configuration, a highly accurate respiratory frequency can be obtained using a cross-correlation function that removes both the noise components contained in the time change in the phase of the radar signal and the noise components contained in the time change in the amplitude of the radar signal.

[0055] (2) In the bioinformation detection device of (1) above, the respiration calculation unit derives the respiration frequency of the subject of bioinformation acquisition by curve fitting a first mathematical model that models the displacement component due to respiration of the subject of bioinformation acquisition to the cross-correlation function.

[0056] (3) The bioinformation detection device of (1) or (2) above further includes a differentiation unit that generates a second-order differential of the cross-correlation function, and a heartbeat calculation unit that derives the heartbeat frequency of the subject of bioinformation acquisition based on the second-order differential of the cross-correlation function.

[0057] In this configuration, the heartbeat frequency can be obtained with high accuracy by using the second derivative of the cross-correlation function from which low-frequency components including displacement components due to respiration have been removed.

[0058] (4) In the bioinformation detection device of (3) above, the heart rate calculation unit applies the respiratory frequency to a first mathematical model and performs curve fitting to the second derivative of the cross-correlation function to derive each variable of the first mathematical model except for the respiratory frequency, applies each variable of the first mathematical model including the respiratory frequency to the first mathematical model, and derives the heart rate frequency of the bioinformation acquisition subject by curve fitting the sum of the first mathematical model and a second mathematical model that models a displacement component due to the heart rate of the bioinformation acquisition subject to the second derivative of the cross-correlation function.

[0059] (5) A biometric information detection method according to one aspect of the present disclosure includes the steps of generating a cross-correlation function between the time change in phase of a radar signal acquired by a radar and the time change in amplitude of the radar signal, and deriving a respiratory frequency of a subject from which biometric information is to be acquired based on the cross-correlation function.

[0060] In this configuration, a highly accurate respiratory frequency can be obtained using a cross-correlation function that removes both the noise components contained in the time change in the phase of the radar signal and the noise components contained in the time change in the amplitude of the radar signal.

[0061] (6) In the bioinformation detection method described above in (5), the respiratory frequency of the subject from which bioinformation is to be obtained is derived by curve fitting a first mathematical model that models the displacement component due to breathing of the subject from which bioinformation is to be obtained to the cross-correlation function.

[0062] (7) The biometric information detection method of (5) or (6) above further includes the steps of generating a second derivative of the cross-correlation function, and deriving a heartbeat frequency of the subject of biometric information acquisition based on the second derivative of the cross-correlation function.

[0063] In this configuration, the heartbeat frequency can be obtained with high accuracy by using the second derivative of the cross-correlation function from which low-frequency components including displacement components due to respiration have been removed.

[0064] (8) In the bioinformation detection method of (7) above, the respiratory frequency is applied to a first mathematical model and curve-fitted to follow the second derivative of the cross-correlation function to derive each variable of the first mathematical model excluding the respiratory frequency, and each variable of the first mathematical model including the respiratory frequency is applied to the first mathematical model, and the sum of the first mathematical model and a second mathematical model that models a displacement component due to the heartbeat of the bioinformation acquisition target is curve-fitted to follow the second derivative of the cross-correlation function to derive the heartbeat frequency of the bioinformation acquisition target.

[0065] According to the present disclosure, it is possible to realize a biological information detection device and a biological information detection method that can improve the accuracy of acquiring biological information.

[0066] REFERENCE SIGNS LIST 1 Biological information detection device 11 Radar 12 Cross-correlation function generation unit 13 Respiration calculation unit 14 Differentiation unit 15 Heart rate calculation unit

Claims

1. A biological information detection device comprising: a radar that emits a transmission wave to a biological information acquisition subject and receives a reflected wave of the transmission wave to acquire a radar signal; a cross-correlation function generation unit that generates a cross-correlation function between a time change in phase of the radar signal and a time change in amplitude of the radar signal; and a respiration calculation unit that derives a respiration frequency of the biological information acquisition subject based on the cross-correlation function.

2. A bioinformation detection device as described in claim 1, wherein the respiration calculation unit derives the respiration frequency of the subject from which the bioinformation is to be obtained by curve fitting a first mathematical model that models the displacement component due to respiration of the subject from which the bioinformation is to be obtained to the cross-correlation function.

3. A bioinformation detection device as claimed in claim 1 or 2, further comprising: a differentiation unit that generates a second derivative of the cross-correlation function; and a heartbeat calculation unit that derives the heartbeat frequency of the subject of bioinformation acquisition based on the second derivative of the cross-correlation function.

4. A bioinformation detection device as described in claim 3, wherein the heart rate calculation unit derives each variable of the first mathematical model except for the respiratory frequency by applying the respiratory frequency to a first mathematical model and curve fitting the curve to the second derivative of the cross-correlation function, and applies each variable of the first mathematical model including the respiratory frequency to the first mathematical model, and derives the heart rate frequency of the subject from which bioinformation is to be obtained by curve fitting the sum of the first mathematical model and a second mathematical model that models a displacement component due to the heart rate of the subject from which bioinformation is to be obtained to the second derivative of the cross-correlation function.

5. A method for detecting biological information, comprising: generating a cross-correlation function between a time change in phase of a radar signal acquired by a radar and a time change in amplitude of the radar signal; and deriving a respiratory frequency of a subject from which biological information is to be acquired based on the cross-correlation function.

6. A bioinformation detection method as claimed in claim 5, comprising the steps of: deriving the respiratory frequency of the subject from which the bioinformation is to be obtained by curve fitting a first mathematical model that models a displacement component due to respiration of the subject from which the bioinformation is to be obtained to the cross-correlation function.

7. A biological information detection method according to claim 5 or 6, further comprising the steps of: generating a second derivative of the cross-correlation function; and deriving a heartbeat frequency of the subject from which the biological information is to be obtained, based on the second derivative of the cross-correlation function.

8. A bioinformation detection method as claimed in claim 7, comprising the steps of: applying the respiratory frequency to a first mathematical model and curve fitting the curve to the second derivative of the cross-correlation function to derive each variable of the first mathematical model excluding the respiratory frequency; applying each variable of the first mathematical model including the respiratory frequency to the first mathematical model; and deriving the heartbeat frequency of the subject from which bioinformation is to be obtained by curve fitting the sum of the first mathematical model and a second mathematical model that models a displacement component due to the heartbeat of the subject from which bioinformation is to be obtained to the second derivative of the cross-correlation function.

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