CN104783777B - The single channel harvester and method of biological electricity and sine wave modulation multiple signals - Google Patents
The single channel harvester and method of biological electricity and sine wave modulation multiple signals Download PDFInfo
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- CN104783777B CN104783777B CN201510196508.8A CN201510196508A CN104783777B CN 104783777 B CN104783777 B CN 104783777B CN 201510196508 A CN201510196508 A CN 201510196508A CN 104783777 B CN104783777 B CN 104783777B
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
- A61B5/318—Heart-related electrical modalities, e.g. electrocardiography [ECG]
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- A—HUMAN NECESSITIES
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- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
- A61B5/369—Electroencephalography [EEG]
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- A61B5/316—Modalities, i.e. specific diagnostic methods
- A61B5/389—Electromyography [EMG]
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
- A61B5/316—Modalities, i.e. specific diagnostic methods
- A61B5/398—Electrooculography [EOG], e.g. detecting nystagmus; Electroretinography [ERG]
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Abstract
The invention discloses a kind of biological electricity and the single channel harvester and method of sine wave modulation multiple signals, the harvester gathers N roads biomedicine signals via analog-digital converter all the way, including is loaded with the high_frequency sine wave and low frequency bioelectrical signals of PPG signals.Current signal is converted into default amplitude voltage signal through current/voltage-converted amplifier, default amplitude bioelectrical signals are obtained by bioelectrical signals detection circuit, default amplitude voltage signal obtains mixed signal with default amplitude bioelectrical signals after adder operation circuit is added, mixed signal is converted into data signal by single channel analog-digital converter, microprocessor is handled data signal, modulated sinusoid signal and low frequency bioelectrical signals are isolated, and multichannel PPG signals are demodulated from modulated sinusoid signal.The characteristics of present invention realizes synchronizes collection to multichannel biomedicine signals via single channel analog-digital converter, and simple with circuit, and cost is cheap and measurement is accurate.
Description
Technical field
The present invention relates to Biomedical Signals Acquisition field, more particularly to a kind of biological electricity and sine wave modulation multiple signals
Single channel harvester and method.
Background technology
The variable quantity of the carrying informations such as voltage signal, is represented in an analogue form in its relaxed state, still, in order to
It is easy to computer disposal, transmission and storage, data signal is generally transformed into by analog-digital converter, therefore cure in biology
Learn in signal transacting, analog-to-digital conversion is essential.
Inventor has found during the present invention is realized, in existing multichannel Biomedical Signals Acquisition, need to generally adopt
With multi-disc ADC or multiway analog switch collocation monolithic ADC scheme, the former has, and circuit is complicated, system power dissipation height and circuit chi
The shortcomings that very little big;And the latter then can be in gatherer process, due to the switching of variable connector, insertion switch noise, and due to more
There is settling time in way switch, can cause to interfere between adjacent channel signals.
The content of the invention
The invention provides a kind of biological electricity and the single channel harvester and method of sine wave modulation multiple signals, the present invention
Analog-to-digital conversion is realized to multichannel biomedicine signals by single channel analog-digital converter, it is described below:
The single channel harvester of a kind of biological electricity and sine wave modulation multiple signals, the single channel harvester include:It is micro-
Processor, the microprocessor export different frequency and into the sine waves of 2 times of ratios, and sine wave drive is at least two kinds of to light
Diode, the light that light emitting diode is sent are received after tested finger by light-sensitive device, and the light-sensitive device is converted into electric current letter
Number, current signal is converted into default amplitude voltage signal through current/voltage-converted amplifier;
The single channel harvester also includes:Low frequency bioelectrical signals detection circuit, adder operation circuit and single channel mould
Number converter;
The low frequency bioelectrical signals detection circuit obtains default amplitude bioelectrical signals, the default amplitude voltage signal
Mixed signal is obtained after the adder operation circuit is added with the default amplitude bioelectrical signals, the mixed signal is by institute
State single channel analog-digital converter and be converted into data signal;
The microprocessor is handled data signal, isolates modulated sinusoid signal and low frequency bioelectrical signals,
And multichannel PPG signals are demodulated from modulated sinusoid signal.
The low frequency bioelectrical signals are specially:Any one in ECG, EEG, EMG, EGG and EOG.
Wherein, the adder operation circuit includes:First resistor and second resistance, one end access the of the first resistor
One signal source, one end access secondary signal source of the second resistance, the other end of the first resistor and the second resistance
Another termination operational amplifier negative polarity input;One end of positive polarity input the 4th resistance of termination of operational amplifier,
The other end ground connection of 4th resistance;The negative polarity input of the operational amplifier also accesses the one of 3rd resistor simultaneously
End, the output end of another termination operational amplifier of the 3rd resistor, output signal voltage.
Another embodiment, the adder operation circuit include:First resistor and second resistance, one end of the first resistor
Access the first signal source, one end access secondary signal source of the second resistance, the other end of the first resistor and described the
The positive polarity input of another termination operational amplifier of two resistance;The negative polarity input of the operational amplifier connects the simultaneously
One end of three resistance and the 4th resistance;The other end ground connection of 4th resistance;Another termination computing of the 3rd resistor is put
The output end of big device, output signal voltage.
A kind of acquisition method for biological electricity and the single channel harvester of sine wave modulation multiple signals, methods described bag
Include following steps:
Mixed signal is converted into data signal by single channel analog-digital converter and is sent into microprocessor;
Microprocessor carries out low-pass filtering treatment to data signal and recovers low frequency bioelectrical signals;Microprocessor is to numeral
Signal enters horizontal lock calculating, separating treatment obtains PPG signals and bioelectrical signals, and the bias light interference in PPG signals is disappeared
Remove;
The valley and peak value of PPG signals are calculated respectively;Again as corresponding to each wavelength of valley and peak computational of PPG signals
Absorbance difference Δ A, the spectral value being made up of absorbance difference Δ A can be obtained.
The microprocessor enters horizontal lock calculating to data signal, separating treatment obtains PPG signals and bioelectrical signals, and
Bias light interference the step of being eliminated in PPG signals is specially:
1) microprocessor control analog-digital converter is assumed to drive the highest frequency f of light emitting diodemax4M speeds pair
Data signal is sampled, sample frequency fs=4M × fmax, sampled signal x (m) is obtained, wherein M is just whole more than or equal to 1
Number;
2) microprocessor is by sample frequency fs=4M × fmaxM times to 4 × f of lower samplingmax;
3) the orthogonal reference sequences y according to caused by sampled signal x (m), microprocessorsAnd y (k)c(k) calculating two is orthogonal
Components RsAnd RC;
The length of sampled signal sequence used in Q expressions;
4) according to quadrature component RsAnd RCThe amplitude A and phase angle theta of data signal are obtained by LPF;
β is M times of some constant value taken of lower sampling;
5) to being sampled 2 times under sampled signal x (m), repeat the 3) step, 4) step continues to calculate frequency and is at half data signal
Amplitude A and phase angle theta, the PPG signals until calculating, having separated whole frequencies.
The beneficial effect of technical scheme provided by the invention is:The present invention is cured by single channel analog-digital converter to multichannel biology
Signal realizes analog-to-digital conversion, and with measurement accuracy is high, circuit structure is simple, device and technological requirement are low, debugging is easy, can
By the advantages that property is high, amount of calculation is small;And when the circuit that adder operation circuit is designed using the present invention, in that context it may be convenient to obtain
The mixed frequency signal high to stable, precision, being easily integrated, and circuit cost is reduced, the dynamic range of signal is expanded, is met
A variety of needs in practical application.
Brief description of the drawings
Fig. 1 is the structural representation of a kind of biological electricity and the single channel harvester of sine wave modulation multiple signals;
Fig. 2 is the structural representation of adder operation circuit;
Fig. 3 is another structural representation of adder operation circuit;
Fig. 4 is the schematic diagram of separation different wave length PPG signals provided by the invention;
Fig. 5 is the flow chart of a kind of biological electricity and the single channel acquisition method of sine wave modulation multiple signals.
In accompanying drawing, the list of parts representated by each label is as follows:
1:Microprocessor; 2:Light emitting diode;
3:Light-sensitive device; 4:Current/voltage-converted amplifier;
5:Low frequency bioelectrical signals detect circuit; 6:Adder operation circuit;
7:Single channel analog-digital converter.
Embodiment
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
It is described in detail on ground.
Embodiment 1
The single channel harvester of a kind of biological electricity and sine wave modulation multiple signals, referring to Fig. 1, the single channel harvester bag
Include:Microprocessor 1, at least two kinds of light emitting diodes 2, light-sensitive device 3, current/voltage-converted amplifier 4, low frequency bioelectrical signals
Circuit 5, adder operation circuit 6 and single channel analog-digital converter 7 are detected,
Microprocessor 1 exports different frequency and into the sine wave of 2 times of ratios, sine wave drive at least two kinds of luminous two
Pole pipe 2, the light that light emitting diode 2 is sent are received after tested finger by light-sensitive device 3, and light-sensitive device 3 is converted into current signal,
Current signal is converted into default amplitude voltage signal through current/voltage-converted amplifier 4.
Low frequency bioelectrical signals detect circuit 5 and obtain default amplitude bioelectrical signals, preset amplitude voltage signal with presetting
Amplitude bioelectrical signals obtain mixed signal after the addition of adder operation circuit 6, and mixed signal is changed by single channel analog-digital converter 7
Into data signal, microprocessor 1 is handled data signal, isolates modulated sinusoid signal and low frequency bioelectrical signals,
And multichannel PPG signals are demodulated from modulated sinusoid signal.
Wherein, the quantity of light emitting diode 2 is more than or equal to 2.During specific implementation, the quantity of light emitting diode 2 is according to reality
Needs in are set;The amplitude of default amplitude voltage signal and default amplitude bioelectrical signals is according in practical application
Needs set, during specific implementation, the embodiment of the present invention is without limitation.
Wherein, low frequency bioelectrical signals include:Any one in the bioelectrical signals such as ECG, EEG, EMG, EGG, EOG.
Microprocessor 1 can use any one in MCU, ARM, DSP or FPGA.Adder operation circuit 6 is using routine on the market
Addition device.
Wherein, the gain of bioelectrical signals detection circuit 5 and bandwidth are by the amplitude and frequency of the bioelectrical signals detected
Scope determines.
Embodiment 2
The single channel harvester of a kind of biological electricity and sine wave modulation multiple signals, referring to Fig. 1, the single channel harvester bag
Include:Microprocessor 1, at least two kinds of light emitting diodes 2, light-sensitive device 3, current/voltage-converted amplifier 4, low frequency bioelectrical signals
Detect circuit 5, adder operation circuit 6 and single channel analog-digital converter 7.The embodiment as different from Example 1, transport by the addition
The adder operation circuit 6 that is designed using the embodiment of the present invention of circuit 6 is calculated to realize, referring to Fig. 2, the adder operation circuit 6 includes:
First resistor R1With second resistance R2,
First resistor R1One end access the first signal source V1, second resistance R2One end access secondary signal source V2, first
Resistance R1The other end and second resistance R2Another termination operational amplifier A negative polarity input;Operational amplifier A is just
The 4th resistance R of polarity input termination4One end, the 4th resistance R4The other end ground connection;The negative polarity input of operational amplifier A
Also access 3rd resistor R simultaneously3One end, 3rd resistor R3Another termination operational amplifier A output end, output signal electricity
Press Vo。
First signal source V1, secondary signal source V2Respectively default amplitude voltage signal and default amplitude bioelectrical signals;
Or, the first signal source V1, secondary signal source V2Respectively default amplitude bioelectrical signals and default amplitude voltage signal;Signal electricity
Press VoFor mixed signal.
Embodiment 3
The single channel harvester of a kind of biological electricity and sine wave modulation multiple signals, referring to Fig. 1, the single channel harvester bag
Include:Microprocessor 1, at least two kinds of light emitting diodes 2, light-sensitive device 3, current/voltage-converted amplifier 4, low frequency bioelectrical signals
Detect circuit 5, adder operation circuit 6 and single channel analog-digital converter 7.The embodiment as different from Example 1, transport by the addition
Calculating circuit 6 can be realized using the adder operation circuit 6 that the embodiment of the present invention designs, referring to Fig. 3, the adder operation circuit 6
Including:First resistor R1With second resistance R2,
First resistor R1One end access the first signal source V1, second resistance R2One end access secondary signal source V2, first
Resistance R1The other end and second resistance R2Another termination operational amplifier A positive polarity input;Operational amplifier A is born
Polarity input meets 3rd resistor R simultaneously3With the 4th resistance R4One end;4th resistance R4The other end ground connection;3rd resistor R3
Another termination operational amplifier A output end, output signal voltage Vo。
First signal source V1, secondary signal source V2Respectively default amplitude voltage signal and default amplitude bioelectrical signals;
Or, the first signal source V1, secondary signal source V2Respectively default amplitude bioelectrical signals and default amplitude voltage signal;Signal electricity
Press VoFor mixed signal.
Embodiment 4
The single channel acquisition method of a kind of biological electricity and sine wave modulation multiple signals, referring to Fig. 4 and Fig. 5, this method includes
Following steps:
101:Mixed signal is converted into data signal by single channel analog-digital converter 7 and is sent into microprocessor 1;
102:Microprocessor 1 carries out low-pass filtering treatment to data signal and recovers low frequency bioelectrical signals;Microprocessor 1
Enter that horizontal lock calculates, separating treatment obtains PPG signals and bioelectrical signals to data signal, and the bias light in PPG signals is done
Disturb and be eliminated;
Wherein, the step is specially:
1) assume that microprocessor 1 controls single channel analog-digital converter 7 to drive the highest frequency f of light emitting diode 2max4M
Speed samples to data signal, sample frequency fs=4M × fmax, obtain sampled signal x (m), wherein M be more than or equal to
1 positive integer;
2) microprocessor 1 is by sample frequency fs=4M × fmaxM times to 4 × f of lower samplingmax;
3) the orthogonal reference sequences y according to caused by sampled signal x (m), microprocessor 1sAnd y (k)c(k) calculating two is orthogonal
Components RsAnd RC;
The length of sampled signal sequence used in Q expressions.
4) according to quadrature component RsAnd RCThe amplitude A and phase angle theta of data signal are obtained by LPF;
β is M times of some constant value taken of lower sampling.
The amplitude A and phase angle theta of the data signal are obtained, namely isolates highest frequency fmaxPPG signals.
5) to being sampled 2 times under sampled signal x (m), repeat the 3) step, 4) step continues to calculate frequency and is at half data signal
Amplitude A and phase angle theta, the PPG signals until calculating, having separated whole frequencies.
Illustrated for the sake of concise explanation by taking 4 kinds of wavelength light emitting diodes 2 as an example, four I/O mouths of microprocessor 1
PX.1, PX.2, PX.3 and PX.4 drive four light emitting diodes by corresponding resistance respectively.What four light emitting diodes were sent
Light is received through tested finger by light sensor 3, and the received signal of light sensor 3 is passed through by operational amplifier A, electricity
Stream/voltage converting amplifiers 4 (being made up of electric capacity and resistance) are converted into default amplitude voltage signal, then single channel analog-digital converter
7 pass through PY mouths to drive the 4M speeds of the highest frequency of light emitting diode 2 that default amplitude voltage signal is converted into data signal
It is sent to microprocessor 1.Data signal first calculates in microprocessor 1, isolates different wave length PPG signals:Obtain each wavelength
PPG signals.
103:The valley and peak value of PPG signals are calculated respectively;Again by each wavelength institute of valley and peak computational of PPG signals
Corresponding absorbance difference Δ A, can be obtained by Δ Aλ1、ΔAλ2……ΔAλnThe spectral value of composition.
Due to the pulsation phenomenon of artery, it is in cyclically-varying to make CBF in blood vessel, and blood is height opaque liquid,
Therefore the change of pulse beating necessarily causes the change of absorbance.
Consider arteries fullness degree minimum state, the incident light from light source not by pulsatile arterial blood absorption, this
When output intensity ImaxIt is most strong, it can be considered the incident light I of pulsatile arterial blood;And arteries fullness degree highest state is corresponding
At the time of the effect of the valley point of photoelectric sphyg ripple, i.e. pulsatile arterial blood is maximum, output intensity I nowminIt is most weak, it is dynamic to pulse
The minimum output intensity I of arteries and veins blood.So filled by recording artery to the maximum absorbance with during arterial contraction to minimum
Value, it is possible to which eliminating skin histology, hypodermis etc., all have shadow of the human body component for absorbance of constant absorption feature
Ring.
If incident intensity is I0, it is respectively I to detect light intensity when light intensity and arterial contraction are detected when artery is fullminAnd Imax,
Absorbance difference during absorbance and arterial contraction when then artery is full is:
Measure the valley I of each photoplethysmographicminAnd peak ImaxIt can obtain corresponding to photoplethysmographic
Absorbance difference Δ A, can obtain by Δ Aλ1、ΔAλ2……ΔAλnThe spectral value of composition.
That is, the valley and peak value of wavelength X 1, λ 2, λ 3 and λ 4 PPG signals are calculated respectively:Iminλ1、Imaxλ1、Iminλ2、
Imaxλ2、Iminλ3、Imaxλ3、Iminλ4And Imaxλ4。
To the model of each device in addition to specified otherwise is done, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned function can be completed.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is only presently preferred embodiments of the present invention, be not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent substitution and improvements made etc., it should be included in the scope of the protection.
Claims (5)
1. the single channel harvester of a kind of biological electricity and sine wave modulation multiple signals, the single channel harvester include:Micro- place
Manage device, the microprocessor exports different frequency and into the sine wave of 2 times of ratios, sine wave drive at least two kinds of luminous two
Pole pipe, the light that light emitting diode is sent are received after tested finger by light-sensitive device, and the light-sensitive device is converted into current signal,
Current signal is converted into default amplitude voltage signal through current/voltage-converted amplifier;Characterized in that,
The single channel harvester also includes:Low frequency bioelectrical signals detection circuit, adder operation circuit and single channel modulus turn
Parallel operation;
The low frequency bioelectrical signals detection circuit obtains default amplitude bioelectrical signals, the default amplitude voltage signal and institute
State default amplitude bioelectrical signals and obtain mixed signal after adder operation circuit addition, the mixed signal is by the list
Road analog-digital converter is converted into data signal;
The microprocessor is handled data signal, isolates modulated sinusoid signal and low frequency bioelectrical signals, and from
Multichannel PPG signals are demodulated in modulated sinusoid signal, are specially:
1) microprocessor controls analog-digital converter to drive the highest frequency f of light emitting diodemax4M speeds to data signal
Sampled, sample frequency fs=4M × fmax, sampled signal x (m) is obtained, wherein M is the positive integer more than or equal to 1;
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3) the orthogonal reference sequences y according to caused by sampled signal x (m), microprocessorsAnd y (k)c(k) two quadrature components are calculated
RsAnd RC;
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The length of sampled signal sequence used in Q expressions;
4) according to quadrature component RsAnd RCThe amplitude A and phase angle theta of data signal are obtained by LPF;
β is M times of some constant value taken of lower sampling;
5) to being sampled 2 times under sampled signal x (m), repeat the 3) step, 4) step continues to calculate frequency and is at half the amplitude of data signal
A and phase angle theta, the PPG signals until calculating, having separated whole frequencies.
2. the single channel harvester of a kind of biological electricity according to claim 1 and sine wave modulation multiple signals, its feature
It is, the low frequency bioelectrical signals are specially:Any one in ECG, EEG, EMG, EGG and EOG.
3. the single channel harvester of a kind of biological electricity according to claim 1 and sine wave modulation multiple signals, its feature
It is, the adder operation circuit includes:First resistor and second resistance,
The first signal source is accessed in one end of the first resistor, one end access secondary signal source of the second resistance, and described the
The negative polarity input of the other end of one resistance and another termination operational amplifier of the second resistance;Operational amplifier is just
One end of polarity input the 4th resistance of termination, the other end ground connection of the 4th resistance;The negative polarity of the operational amplifier is defeated
Enter end also while access one end of 3rd resistor, the output end of another termination operational amplifier of the 3rd resistor, output letter
Number voltage.
4. the single channel harvester of a kind of biological electricity according to claim 1 and sine wave modulation multiple signals, its feature
It is, the adder operation circuit includes:First resistor and second resistance,
The first signal source is accessed in one end of the first resistor, one end access secondary signal source of the second resistance, and described the
The positive polarity input of the other end of one resistance and another termination operational amplifier of the second resistance;The operational amplifier
Negative polarity input connect one end of 3rd resistor and the 4th resistance simultaneously;The other end ground connection of 4th resistance;Described
The output end of another termination operational amplifier of three resistance, output signal voltage.
A kind of 5. single channel of biological electricity being used in claim 1-4 described in any claim and sine wave modulation multiple signals
The acquisition method of harvester, it is characterised in that the described method comprises the following steps:
Mixed signal is converted into data signal by single channel analog-digital converter and is sent into microprocessor;
Microprocessor carries out low-pass filtering treatment to data signal and recovers low frequency bioelectrical signals;Microprocessor is to data signal
Enter that horizontal lock calculates, separating treatment obtains PPG signals and bioelectrical signals, and the bias light interference in PPG signals is eliminated;
The valley and peak value of PPG signals are calculated respectively;Again as the suction corresponding to each wavelength of valley and peak computational of PPG signals
Luminosity difference DELTA A, the spectral value being made up of absorbance difference Δ A can be obtained;
The microprocessor enters horizontal lock calculating to data signal, separating treatment obtains PPG signals and bioelectrical signals, and PPG
Bias light interference the step of being eliminated in signal is specially:
1) microprocessor controls analog-digital converter to drive the highest frequency f of light emitting diodemax4M speeds to data signal
Sampled, sample frequency fs=4M × fmax, sampled signal x (m) is obtained, wherein M is the positive integer more than or equal to 1;
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<mo>+</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>l</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>......</mn>
</mrow>
2) microprocessor is by sample frequency fs=4M × fmaxM times to 4 × f of lower samplingmax;
3) the orthogonal reference sequences y according to caused by sampled signal x (m), microprocessorsAnd y (k)c(k) two quadrature components are calculated
RsAnd RC;
<mrow>
<msub>
<mi>R</mi>
<mi>s</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>Q</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mo>&lsqb;</mo>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mi>m</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mi>m</mi>
<mo>+</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mi>C</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>Q</mi>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mo>&lsqb;</mo>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mi>m</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mi>m</mi>
<mo>+</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
The length of sampled signal sequence used in Q expressions;
4) according to quadrature component RsAnd RCThe amplitude A and phase angle theta of data signal are obtained by LPF;
β is M times of some constant value taken of lower sampling;
5) to being sampled 2 times under sampled signal x (m), repeat the 3) step, 4) step continues to calculate frequency and is at half the amplitude of data signal
A and phase angle theta, the PPG signals until calculating, having separated whole frequencies.
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