CN107149470A - A kind of gynemetrics's electronic pulse meter control system based on internet - Google Patents
A kind of gynemetrics's electronic pulse meter control system based on internet Download PDFInfo
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- CN107149470A CN107149470A CN201710050908.7A CN201710050908A CN107149470A CN 107149470 A CN107149470 A CN 107149470A CN 201710050908 A CN201710050908 A CN 201710050908A CN 107149470 A CN107149470 A CN 107149470A
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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
- A61B5/02—Detecting, measuring or recording pulse, heart rate, blood pressure or blood flow; Combined pulse/heart-rate/blood pressure determination; Evaluating a cardiovascular condition not otherwise provided for, e.g. using combinations of techniques provided for in this group with electrocardiography or electroauscultation; Heart catheters for measuring blood pressure
- A61B5/024—Detecting, measuring or recording pulse rate or heart rate
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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
- A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
- A61B5/7203—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal
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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
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Abstract
The present invention relates to a kind of gynemetrics's electronic pulse meter control system based on internet, including display module, the display module is connected with data reception module, the data reception module is connected with the Internet module, the Internet module makes comprehensive accurate analysis result for being connected real-time interactive with internet, the Internet module is connected with digital circuit blocks, the analog signal that the digital circuit blocks are used to receive sensor assembly is converted into data signal and is sent to the Internet module, the digital circuit blocks are connected with sensor assembly, the sensor assembly is used to measure beat pulse and exports analog signal, the sensor assembly is connected with medical device module, the medical device module is used to contact patient measuring point and electric energy is provided and stored for total system.The present invention makes comprehensive accurate analysis result by the connection real-time interactive to internet, realizes the reliable accuracy of measurement result.
Description
Technical field
The invention belongs to Internet technology and the crossing domain of medical sanitary technology, more particularly to it is a kind of based on internet
Gynemetrics's electronic pulse meter control system.
Background technology
Mobile communication technology refers to merge mobile communication technology and medical sanitary technology with medical sanitary technology
One complex art of development.Application and concentrated reflection of the mobile communication technology in medical science are that application communication technology is realized far
Journey medical science and Medical Information Resources it is shared, and the measurement of pulse is an essential project for patient, in woman's production
Section field is particularly important, and many diseases particularly heart disease clinically etc. can all make pulse change, in cardiac cycle, by
It is critical in the beating state of an illness of ventricular contraction and the expansion of the alternately vascular generating period of diastole and return, it is particularly approaching one's end
Obvious change can all occur for the number of times and pulse frequency of preceding pulse, and feeling the pulse is more considered as the main method of diagnosis and treatment disease by the traditional Chinese medical science, side by side
For one of " four methods of diagnosis " basic methods, the heart of puerpera bears parent and two people of child simultaneously, and what pulse was changed is timely
Effective assurance and observation just seem very crucial and important.
Traditional pulses measure method, main to be pressed in using forefinger and middle finger at radial artery, dynamics is moderate, can feel arteries and veins
Beating, our arm is easily put on desktop, is not limited to certainly on desktop, can also be placed on the leg of oneself, only
It is convenient for measuring just, time of measuring is 30 seconds, then will measure beat pulse number of times and be multiplied by 2, is exactly our one minute pulse
The number of times of bounce, the method needs the regular hour to ensure, and is influenceed larger by our mental and physical, has often measured partially
The beat pulse number of times of difference.In recent years, the pulses measure of puerpera is increasingly valued by people, and current gynemetrics field is badly in need of
A kind of convenient and swift, efficiently and accurately, error rate are low, the advanced pulse measurement device of means.
The content of the invention
The present invention for solve technical problem present in known technology provide a kind of easy to use, measurement accurately, data
Clearly gynemetrics's electronic pulse meter control system based on internet.
The present invention is adopted the technical scheme that to solve technical problem present in known technology:
Gynemetrics's electronic pulse meter control system based on internet that the present invention is provided, woman's production based on internet
Section's electronic pulse meter control system includes display module;
The display module is used to receive data from data reception module and shown;
The display module is connected with data reception module;
The data reception module is used to receive the various data that the Internet module is sent;
The data reception module is connected with the Internet module;
The Internet module makes comprehensive accurate analysis result for being connected real-time interactive with internet;
The Internet module is connected with digital circuit blocks, and the digital circuit blocks are used to receive sensor assembly
Analog signal is converted into data signal and is sent to the Internet module, and the digital circuit blocks are connected with sensor assembly;
The sensor assembly is used to measure beat pulse and exports analog signal, the sensor assembly and Medical Devices
Module is connected, and the medical device module is used to contact patient measuring point and electric energy is provided and stored for total system;Sensing
Device module includes pulses measure sensors A and pulses measure sensor B;Time alignment process complete sensing data between when
Between on alignment, the metric data of pulses measure sensors A, pulses measure sensor B under local rectangular coordinate system is respectively
YA(ti) and YB(ti), and pulses measure sensors A sample frequency be more than pulses measure sensor B sample frequency, then by
Pulses measure sensors A carries out registration to pulses measure sensor B sampling instant, is specially:
The temporal registration algorithm extrapolated using interpolation is by the sampled data of pulses measure sensors A to pulses measure sensor
B data carry out registration so that two sensors have synchronous metric data, interpolation at the spatial registration moment to same target
Temporal registration algorithm of extrapolating is as follows:
Each sensor observation data are subjected to increment sequence by measurement accuracy in same timeslice, then by pulses measure
The observation data of sensors A are a series of equally spaced to be formed respectively to pulses measure sensor B time point interpolation, extrapolation
Target observation data, obtain pulses measure using the carry out interpolation extrapolation temporal registration algorithm of 3 conventional parabolic interpolations and pass
Sensor A is in tBkMeasuring value of the moment under local rectangular coordinate systemFor:
Wherein, tBkFor registering moment, tk-1,tk,tk+1For the pulses measure sensors A distance registering moment, three recently adopt
Sample moment, YA(tk-1),YA(tk),YA(tk+1) it is respectively its corresponding detection data to target;
After deadline registration, according to the registration data of pulses measure sensors A and pulses measure sensor B sampling
Data, arteries and veins is realized using based on the pseudo- measurement method under solid (Earth Center Earth Fixed, the ECEF) coordinate system of ground heart
The estimation of measurement sensor of fighting A and pulses measure sensor B systematic error;Systematic error estimation algorithm tool based on ECEF
Body is:
Assuming that k moment target actual position under local rectangular coordinate system is X'1(k)=[x'1(k),y'1(k),z'1
(k)]T, corresponding measuring value is under polar coordinate systemRespectively distance, azimuth, the angle of pitch;Conversion is extremely
It is X under local rectangular coordinate system1(k)=[x1(k),y1(k),z1(k)]T;Sensing system deviation isRespectively distance, the systematic error of azimuth and the angle of pitch;Then have
WhereinObservation noise is represented, average is that zero, variance is
Formula (1) can be deployed with first approximation and be write as matrix form:
X'1(k)=X1(k)+C(k)[ξ(k)+n(k)] (12)
Wherein,
If two pulses measure sensors As and B, then (set for same public target under ECEF coordinate system as X'e
=[x'e,y'e,z'e]T), it can obtain
X'e=XAs+BAX'A1(k)=XBs+BBX'B1(k) (13)
BA, BBChange respectively position of the target under pulses measure sensors A and pulses measure sensor B local coordinate systems
Transition matrix during position under to ECEF coordinate systems;
Definition puppet, which is measured, is:
Z (k)=XAe(k)-XBe(k) (14)
Wherein, XAe(k)=XAs+BAXA1(k);XBe(k)=XBs+BBXB1(k)
Formula (2), formula (3) substitution formula (4) can be obtained into the pseudo-measurement on sensor bias
Z (k)=H (k) β (k)+W (k) (15)
Wherein,Z (k) is pseudo-measurement vector;H (k) is calculation matrix;β is
Sensor bias vector;W (k) is measurement noise vector;Due to nA(k),nB(k) it is random for zero-mean, separate Gaussian
Variable, therefore W (k) is equally zero-mean gaussian type stochastic variable, its covariance matrix is R (k);
The digital circuit blocks include adjusting module and amplification module, and the electric module of the adjustment is used for conversion sensor mould
The analog signal that block is sent is data signal, and the amplification module is used to amplify data signal and be sent to the Internet module;
The medical device module includes power supply module and electricity storage module, and the power supply module is used to provide whole system
Electric energy, the electricity storage module is used to store electric energy for whole system.
Further, the measurement model of the pulses measure sensors A is as follows:
YA(tk-1)、YA(tk)、YA(tk+1) be respectively pulses measure sensors A to target in tk-1,tk,tk+1Moment it is local
Measuring value under cartesian coordinate system, be respectively:
Wherein, Y 'A(tk-1)、Y′A(tk)、Y′A(tk+1) it is respectively pulses measure sensors A in tk-1, tk, tk+1The sheet at moment
Actual position under ground cartesian coordinate system;CA(t) it is the transformation matrix of error;ξA(t) it is the systematic error of sensor;
For system noise, it is assumed thatFor zero-mean, separate Gaussian stochastic variable, noise covariance
Matrix is respectively RA(k-1)、RA(k)、RA(k+1)。
Further, the digital circuit blocks are to frequency-hopping mixing signal time-frequency domain matrixPre-processed, specifically include following two step:
The first step is rightProgress goes low energy to pre-process, i.e., in each sampling instant
P, willThe value that amplitude is less than thresholding ε is set to 0, and is obtainedThresholding ε setting can be determined according to the average energy of signal is received;
Second step, finds out the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero, usesRepresent, whereinRepresent the response of p moment time-frequencyThese non-zeros are normalized and pre-processed, obtained by corresponding frequency indices when non-zero
Pretreated vectorial b (p, q)=[b1(p, q), b2(p, q) ..., bM(p, q)]T, wherein
The present invention has the advantages and positive effects of:Because the present invention is made by the connection real-time interactive to internet
Comprehensive accurate analysis result, realizes the reliable accuracy of measurement result;Display module realizes the clear exhibition of measurement data
It is existing, it is ensured that the observability of measurement result;Power supply module is realized by electrical power storage, improves the continuation of the journey of control system
Ability.
Brief description of the drawings
Fig. 1 is the structural representation of gynemetrics's electronic pulse meter control system provided in an embodiment of the present invention based on internet
Figure.
In figure, 1, display module;2nd, data reception module;3rd, the Internet module;4th, data signal module;5th, sensor die
Block, 6, medical device module;7th, puerpera;8th, power supply module;9th, electricity storage module;10th, adjusting module;11st, amplification module.
Embodiment
In order to further understand the content, features and effects of the present invention, hereby enumerating following examples, and coordinate accompanying drawing
Describe in detail as follows.
The structure of the present invention is explained in detail with reference to Fig. 1.
Gynemetrics's electronic pulse meter control system provided in an embodiment of the present invention based on internet, including display module 1,
The display module 1 is used to receive data from data reception module 2 and shown, the display module 1 and data reception
Block 2 is connected, and the data reception module 2 is used to receive the various data that the Internet module 3 is sent, the data reception module
2 are connected with the Internet module 3, and the Internet module 3 makes comprehensive accurate analysis for being connected real-time interactive with internet
As a result, the Internet module 3 is connected with digital circuit blocks 4, and the digital circuit blocks 4 include adjusting module 10 and amplification
Module 11, the adjusting module 10 is data signal, the amplification module for the analog signal that conversion sensor module 5 is sent
11 are used to amplify data signal and be sent to the Internet module 3, and the digital circuit blocks 4 are used to receive sensor assembly 5
Analog signal be converted into data signal and be sent to the Internet module 3, the digital circuit blocks 4 connect with sensor assembly 5
Connect, the sensor assembly 5 is used to measure beat pulse and exports analog signal, the sensor assembly 5 and Medical Devices mould
Block 6 is connected, and the medical device module 6 includes power supply module 8 and electricity storage module 9, and the power supply module 8 is used for whole system
Electric energy is provided, the electricity storage module 9 is used to store electric energy for whole system, and the medical device module 6 is used to contact patient's survey
Amount position simultaneously provides and stored electric energy for total system.
Sensor assembly 5 includes pulses measure sensors A and pulses measure sensor B;Time alignment process completes sensing
Alignment between device data in time, pulses measure sensors A, pulses measure sensor B are under local rectangular coordinate system
Metric data is respectively YA(ti) and YB(ti), and the sample frequency of pulses measure sensors A is more than pulses measure sensor B's
Sample frequency, then carry out registration from pulses measure sensors A to pulses measure sensor B sampling instant, is specially:
The temporal registration algorithm extrapolated using interpolation is by the sampled data of pulses measure sensors A to pulses measure sensor
B data carry out registration so that two sensors have synchronous metric data, interpolation at the spatial registration moment to same target
Temporal registration algorithm of extrapolating is as follows:
Each sensor observation data are subjected to increment sequence by measurement accuracy in same timeslice, then by pulses measure
The observation data of sensors A are a series of equally spaced to be formed respectively to pulses measure sensor B time point interpolation, extrapolation
Target observation data, obtain pulses measure using the carry out interpolation extrapolation temporal registration algorithm of 3 conventional parabolic interpolations and pass
Sensor A is in tBkMeasuring value of the moment under local rectangular coordinate systemFor:
Wherein, tBkFor registering moment, tk-1,tk,tk+1For the pulses measure sensors A distance registering moment, three recently adopt
Sample moment, YA(tk-1),YA(tk),YA(tk+1) it is respectively its corresponding detection data to target;
After deadline registration, according to the registration data of pulses measure sensors A and pulses measure sensor B sampling
Data, arteries and veins is realized using based on the pseudo- measurement method under solid (Earth Center Earth Fixed, the ECEF) coordinate system of ground heart
The estimation of measurement sensor of fighting A and pulses measure sensor B systematic error;Systematic error estimation algorithm tool based on ECEF
Body is:
Assuming that k moment target actual position under local rectangular coordinate system is X'1(k)=[x'1(k),y'1(k),z'1
(k)]T, corresponding measuring value is under polar coordinate systemRespectively distance, azimuth, the angle of pitch;Conversion is extremely
It is X under local rectangular coordinate system1(k)=[x1(k),y1(k),z1(k)]T;Sensing system deviation isRespectively distance, the systematic error of azimuth and the angle of pitch;Then have
WhereinObservation noise is represented, average is that zero, variance is
Formula (1) can be deployed with first approximation and be write as matrix form:
X'1(k)=X1(k)+C(k)[ξ(k)+n(k)] (21)
Wherein,
If two pulses measure sensors As and B, then (set for same public target under ECEF coordinate system as X'e
=[x'e,y'e,z'e]T), it can obtain
X'e=XAs+BAX'A1(k)=XBs+BBX'B1(k) (22)
BA, BBChange respectively position of the target under pulses measure sensors A and pulses measure sensor B local coordinate systems
Transition matrix during position under to ECEF coordinate systems;
Definition puppet, which is measured, is:
Z (k)=XAe(k)-XBe(k) (23)
Wherein, XAe(k)=XAs+BAXA1(k);XBe(k)=XBs+BBXB1(k)
Formula (2), formula (3) substitution formula (4) can be obtained into the pseudo-measurement on sensor bias
Z (k)=H (k) β (k)+W (k) (24)
Wherein,Z (k) is pseudo-measurement vector;H (k) is calculation matrix;β is
Sensor bias vector;W (k) is measurement noise vector;Due to nA(k),nB(k) it is random for zero-mean, separate Gaussian
Variable, therefore W (k) is equally zero-mean gaussian type stochastic variable, its covariance matrix is R (k).
Further, the measurement model of the pulses measure sensors A is as follows:
YA(tk-1)、YA(tk)、YA(tk+1) be respectively pulses measure sensors A to target in tk-1,tk,tk+1Moment it is local
Measuring value under cartesian coordinate system, be respectively:
Wherein, Y'A(tk-1)、Y'A(tk)、Y'A(tk+1) it is respectively pulses measure sensors A in tk-1,tk,tk+1The sheet at moment
Actual position under ground cartesian coordinate system;CA(t) it is the transformation matrix of error;ξA(t) it is the systematic error of sensor;
For system noise, it is assumed thatFor zero-mean, separate Gaussian stochastic variable, noise covariance
Matrix is respectively RA(k-1)、RA(k)、RA(k+1)。
Further, the digital circuit blocks are to frequency-hopping mixing signal time-frequency domain matrixPre-processed, specifically include following two step:
The first step is rightProgress goes low energy to pre-process, i.e., in each sampling instant
P, willThe value that amplitude is less than thresholding ε is set to 0, and is obtainedThresholding ε setting can be determined according to the average energy of signal is received;
Second step, finds out the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero, usesRepresent, whereinRepresent the response of p moment time-frequencyThese non-zeros are normalized and pre-processed, obtained by corresponding frequency indices when non-zero
Pretreated vectorial b (p, q)=[b1(p,q),b2(p,q),…,bM(p,q)]T, wherein
Operation principle:In use, the power supply module 8 in medical device module 6 provides electric energy, electricity storage module to whole system
9 be that whole system stores electric energy, and the measurement beat pulse of sensor assembly 5 simultaneously exports the tune in analog signal, digital circuit blocks 4
The analog signal that the conversion sensor module 5 of mould preparation block 10 is sent is data signal, and data signal is amplified concurrent by amplification module 11
The Internet module 3 is given, the Internet module 3 is connected real-time interactive with internet and makes comprehensive accurate analysis result, and data connect
Receive module 2 and receive the various data that the Internet module 3 is sent, display module 1 receives data from data reception module 2 and shown
Out, it is ensured that the observability of measurement result.
It is described above to be only the preferred embodiments of the present invention, any formal limitation not is made to the present invention,
Every technical spirit according to the present invention is belonged to any simple modification made for any of the above embodiments, equivalent variations and modification
In the range of technical solution of the present invention.
Claims (3)
1. a kind of gynemetrics's electronic pulse meter control system based on internet, it is characterised in that the woman based on internet
Obstetrics' electronic pulse meter control system includes display module;
The display module is used to receive data from data reception module and shown;
The display module is connected with data reception module;
The data reception module is used to receive the various data that the Internet module is sent;
The data reception module is connected with the Internet module;
The Internet module makes comprehensive accurate analysis result for being connected real-time interactive with internet;
The Internet module is connected with digital circuit blocks, and the digital circuit blocks are used for the simulation for receiving sensor assembly
Signal is converted into data signal and is sent to the Internet module, and the digital circuit blocks are connected with sensor assembly;
The sensor assembly is used to measure beat pulse and exports analog signal, the sensor assembly and medical device module
Connection, the medical device module is used to contact patient measuring point and electric energy is provided and stored for total system;Sensor die
Block includes pulses measure sensors A and pulses measure sensor B;Between time alignment process completion sensing data in time
Alignment, the metric data of pulses measure sensors A, pulses measure sensor B under local rectangular coordinate system is respectively YA(ti)
And YB(ti), and sample frequency of the sample frequency more than pulses measure sensor B of pulses measure sensors A, then by pulses measure
Sensors A carries out registration to pulses measure sensor B sampling instant, is specially:
The temporal registration algorithm extrapolated using interpolation is by the sampled data of pulses measure sensors A to pulses measure sensor B's
Data carry out registration so that two sensors have at the spatial registration moment to same target outside synchronous metric data, interpolation
Push away temporal registration algorithm as follows:
Each sensor observation data are subjected to increment sequence by measurement accuracy in same timeslice, then pulses measure are sensed
Device A observation data are respectively to pulses measure sensor B time point interpolation, extrapolation, to form a series of equally spaced targets
Data are observed, pulses measure sensor is obtained using the carry out interpolation extrapolation temporal registration algorithm of 3 conventional parabolic interpolations
A is in tBkMeasuring value of the moment under local rectangular coordinate systemFor:
Wherein, tBkFor registering moment, tk-1,tk,tk+1During for three nearest samplings of pulses measure sensors A distance registering moment
Carve, YA(tk-1),YA(tk),YA(tk+1) it is respectively its corresponding detection data to target;
After deadline registration, according to the registration data of pulses measure sensors A and pulses measure sensor B sampled data,
Pulses measure is realized using based on the pseudo- measurement method under solid (Earth Center Earth Fixed, the ECEF) coordinate system of ground heart
The estimation of sensors A and pulses measure sensor B systematic error;Systematic error estimation algorithm based on ECEF is specially:
Assuming that k moment target actual position under local rectangular coordinate system is X'1(k)=[x'1(k),y'1(k),z'1(k)]T, pole
Corresponding measuring value is under coordinate systemRespectively distance, azimuth, the angle of pitch;Change to local straight
It is X under angular coordinate system1(k)=[x1(k),y1(k),z1(k)]T;Sensing system deviation isRespectively distance, the systematic error of azimuth and the angle of pitch;Then have
WhereinObservation noise is represented, average is that zero, variance is
Formula (1) can be deployed with first approximation and be write as matrix form:
X'1(k)=X1(k)+C(k)[ξ(k)+n(k)] (3)
Wherein,
If two pulses measure sensors As and B, then (set for same public target under ECEF coordinate system as X'e=
[x'e,y'e,z'e]T), it can obtain
X'e=XAs+BAX'A1(k)=XBs+BBX'B1(k) (4)
BA, BBRespectively target is transformed into pulses measure sensors A with the position under pulses measure sensor B local coordinate systems
Transition matrix during position under ECEF coordinate systems;
Definition puppet, which is measured, is:
Z (k)=XAe(k)-XBe(k) (5)
Wherein, XAe(k)=XAs+BAXA1(k);XBe(k)=XBs+BBXB1(k)
Formula (2), formula (3) substitution formula (4) can be obtained into the pseudo-measurement on sensor bias
Z (k)=H (k) β (k)+W (k) (6)
Wherein,Z (k) is pseudo-measurement vector;H (k) is calculation matrix;β is sensing
Device bias vector;W (k) is measurement noise vector;Due to nA(k),nB(k) become at random for zero-mean, separate Gaussian
Amount, therefore W (k) is equally zero-mean gaussian type stochastic variable, its covariance matrix is R (k);
The digital circuit blocks include adjusting module and amplification module, and the electric module of the adjustment is sent out for conversion sensor module
The analog signal come is data signal, and the amplification module is used to amplify data signal and be sent to the Internet module;
The medical device module includes power supply module and electricity storage module, and the power supply module is used to provide electricity to whole system
Can, the electricity storage module is used to store electric energy for whole system.
2. gynemetrics's electronic pulse meter control system as claimed in claim 1 based on internet, it is characterised in that the arteries and veins
Measurement sensor of fighting A measurement model is as follows:
YA(tk-1)、YA(tk)、YA(tk+1) be respectively pulses measure sensors A to target in tk-1,tk,tk+1The local flute card at moment
Measuring value under your coordinate system, be respectively:
Wherein, Y'A(tk-1)、Y'A(tk)、Y'A(tk+1) it is respectively pulses measure sensors A in tk-1,tk,tk+1The local flute at moment
Actual position under karr coordinate system;CA(t) it is the transformation matrix of error;ξA(t) it is the systematic error of sensor;To be
System noise, it is assumed thatFor zero-mean, separate Gaussian stochastic variable, noise covariance matrix
Respectively RA(k-1)、RA(k)、RA(k+1)。
3. gynemetrics's electronic pulse meter control system as claimed in claim 1 based on internet, it is characterised in that the number
Word circuit module is to frequency-hopping mixing signal time-frequency domain matrixPre-processed, specific bag
Include following two step:
The first step is rightProgress goes low energy to pre-process, i.e., in each sampling instant p, willThe value that amplitude is less than thresholding ε is set to 0, and is obtained
Thresholding ε setting can be determined according to the average energy of signal is received;
Second step, finds out the time-frequency numeric field data of p moment (p=0,1,2 ... P-1) non-zero, usesRepresent, whereinRepresent the response of p moment time-frequencyThese non-zeros are normalized and pre-processed, obtained by corresponding frequency indices when non-zero
Pretreated vectorial b (p, q)=[b1(p,q),b2(p,q),…,bM(p,q)]T, wherein
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