CN102393870A - Modification method for uneven pulse wave data base line - Google Patents

Modification method for uneven pulse wave data base line Download PDF

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CN102393870A
CN102393870A CN201110161081XA CN201110161081A CN102393870A CN 102393870 A CN102393870 A CN 102393870A CN 201110161081X A CN201110161081X A CN 201110161081XA CN 201110161081 A CN201110161081 A CN 201110161081A CN 102393870 A CN102393870 A CN 102393870A
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pulse wave
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CN102393870B (en
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蔡觉平
曾祥云
赵连锋
袁念德
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Xidian University
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Abstract

The invention discloses a modification method for an uneven pulse wave data base line, and technical problem of uneven original data base line collected by a pulse sensor can be solved. The method comprises the following steps that: firstly, original data for a pulse is input, and pulse wave periods contained in the original pulse data can be distinguished and divided; under the circumstance of small data quantity, a cubic polynominal fitting method is adopted, a polynominal function discretization is fitted, and data is corrected to be (xj, yj- yyj); under the circumstance of large data quantity, a section cubic spline interpolation manner is adopted, difference is carried out for minimum value points of all pulse wave periods, and a difference function s=s (x) can be obtained, yyj =ss (xj) can be obtained through discretization; and the data is corrected to be (xj, yj-yyj). In the modification method, the base line is corrected, pulse condition information can be effectively protected at the same time, calculated quantity is small, modification effect is good, circumstances of large data quantity and small data quantity can be corrected, the modification method is particularly applicable to the conventional pulse condition collecting and analyzing equipment, and moreover, novel hardware equipment is not needed to be configured and added.

Description

The modification method that pulse wave data baseline is uneven
Technical field
The invention belongs to the electronic medical instruments technical field; Relating generally to pulse wave signal handles; Relate in particular to a kind of modification method of the raw data that pulse transducer is gathered; Being that the uneven phenomenon of raw data baseline that pulse transducer collects is revised, specifically is the uneven modification method of a kind of pulse wave data baseline.The present invention need not reequip or add new hardware device just can be used for existing pulse-tracing collection analytical equipment.
Background technology
Pulse wave spectrum is a kind of important method of tcm diagnosis, but there are the characteristics of " clear, as to refer to down difficult name " in the heart in traditional pulse wave spectrum method, is difficult for accomplishing objective and fair.For pulse wave spectrum is objectified more; Relevant scholar has done a lot of researchs, as utilizes pulse transducer to gather pulse information, with rendering computer arteries and veins figure; Algorithm for design extracts pathology, the physiologic information in the pulse condition, sets up the robotization of diagnosis by feeling the pulse database realization diagnosis by feeling the pulse etc.Wherein, utilizing pulse transducer that pulse wave signal is gathered accurately is the requisite basis of realizing that diagnosis by feeling the pulse objectifies.
At present, the researchist has developed multiple pulse transducer and some can further be discerned, analyze the pathology, the physiologic information instrument that contain in the pulse condition, like HK2000G pulse transducer, electropulsograph etc.But the uneven phenomenon of baseline appears in pulse data sometimes that utilize present sensor acquisition to arrive, the phenomenon that baseline is uneven or because measured's breathing influence, action influence, or produce owing to acquisition instrument is affected by the external environment, referring to Fig. 2.Area I and area I I partly have the epirelief trend of arch among the figure, are unfavorable for the Chinese medicine pulse information that comprises in the pulse signal is further analyzed.
The main method that traditional solution baseline is uneven has:
Method 1: filter method.This method is the baseline correction method of using always, but this method is lost the pulse condition information that contains in the pulse signal easily, causes follow-up analysis to pulse condition inaccurate.
Method 2: Wavelet Transform.This precision of method is than higher, but the baseline correction method operand of wavelet transformation is bigger, and yardstick is selected also more complicated, is difficult to apply.
Method 3: polynomial fitting method.For fear of the imperial lattice phenomenon of high-order moment, cubic polynomial is often adopted in the general polynomial match.At this moment, if data are long, the fitting effect of carrying out data fitting with cubic polynomial is often undesirable.
Method 4: method of interpolation.This method need at first be extracted some points, but could more preferably to show the drift situation be this method condition precedent accurately about extracting which point.This method has advantage when the bigger situation of deal with data amount.
The technology that present existing processing pulse wave data baseline is uneven can not be handled the uneven problem of data baseline that the pulse collection instrument is gathered well under the prerequisite of effectively protecting pulse condition information.
Summary of the invention
There is the phenomenon of baseline wander sometimes in the data that the present invention is directed to the pulse transducer collection; Propose a kind ofly can effectively protect pulse condition information; Calculated amount is little, and correction effect is good, to the modification method of the big pulse wave data baseline injustice that all can revise with the little different situations of data volume of data volume; Be specially adapted in the existing pulse analysis equipment, and need not reequip or add new hardware device.
The present invention is the uneven modification method of a kind of pulse wave data baseline, mainly is that the baseline of pulse transducer image data is revised, and comprises the steps:
A. import the original pulse data (x that gathers by pulse transducer j, y j), the pulse wave cycle that these data comprise is no less than 3;
B. discern and divide the pulse wave cycle that comprises in the original pulse data, the division of each pulse wave cycle is a separation with the decent end in each cycle, and separation is exactly the minimum point of each pulse wave, obtains the minimum point (xc of each pulse wave in the raw data j, yc j) and number N;
C. if N<7, then carry out data correction based on fitting of a polynomial: according to least square method to raw data (x j, y j) carry out fitting of a polynomial, obtain polynomial function
Figure BSA00000518091000021
In each fitting coefficient a i, x is the polynomial expression independent variable in the formula, and P is a dependent variable, and n is the degree of polynomial, and for fear of the imperial lattice phenomenon of high-order moment, the general value of n is 3, with x jBring polynomial function into
Figure BSA00000518091000022
Carry out the polynomial function discretize,
Figure BSA00000518091000023
Make Y j=y j-yy j, raw data is modified to (x j, Y j), carry out step e then; If step D is then carried out in N>=7;
D. if the data correction based on the segmentation cubic spline interpolation is then carried out: with (the xc that discerns among the step B in N>=7 j, yc j) be interpolation point, construct and find the solution segmentation cubic spline functions s=s (x), to raw data (x j, y j), with x jBring among the segmentation cubic spline functions s=s (x) and carry out the function discretize, get yy j=s (x j), make Y j=y j-yy j, raw data is modified to (x j, Y j), carry out step e;
E. obtain the pulse wave data (x of unified baseline j, Y j), with this revised pulse data as output.Because the effective information in the pulse data is the amplitude of pulse wave, promptly with respect to the relative size of data minimum value, so the present invention can not cause losing of pulse condition information to the modification of overall data absolute size.
The present invention is based on data fitting and data interpolating method, be used for the pulse-tracing collection analytical equipment, can solve the uneven problem of data baseline well.The situation that the present invention is little to data volume; Adopt the baseline modification method of data fitting; The situation big to data volume, the baseline modification method of employing data interpolating has enlarged the use and the scope of application; The drift of baseline appears in the data that efficiently solve the pulse transducer collection, has also kept the pulse condition information that contains in the original pulse wave well.
Realization of the present invention also is: the described identification of step B is also divided the method for the pulse wave cycle that comprises in the original pulse data, comprises the steps:
2.1. make loop variable i=i 0, i 0=round (0.4f 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes x round, x=0.4f here 0, expression need be to 0.4f 0Round;
2.2. compare the ordinate and the (i before it of i data points 0-1) individual data and (i thereafter 0-1) size of individual data ordinate if the ordinate of these data is minimum value, then writes down the i value, makes i=i+jump then, jump=round (0.3f 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes the x round, otherwise makes i=i+1;
2.3. if i<T-i 0-1, then repeating step 2.2, otherwise carry out steps 2.4, total number at the original Pulse Rate strong point that T representes to import in the formula;
2.4. all i values of discerning successively and writing down in the output step 2.2, these values are exactly horizontal ordinate xc corresponding to the division separation of each pulse cycle in raw data i
In the above-mentioned steps process of identification, division pulse wave cycle has been taked acceleration scheme: after the minimum value that recognizes a pulse wave cycle; With skipping the minimum value that follow-up some spots continues to discern next pulse wave cycle again; Because can not occur the minimum value of next pulse wave cycle in some points of next-door neighbour; The division speed of pulse wave cycle has been improved greatly, also is that basis has accurately been established in follow-up identification and correction.
Realization of the present invention also is: the described data correcting method based on fitting of a polynomial of step C comprises the steps:
3.1 according to raw data (x j, y j), separate about a iSystem of equations:
Figure BSA00000518091000041
Obtain coefficient a i, and then polynomial fitting is arranged p = Σ i = 0 n a i x i ;
3.2 with raw data (x i, y i) in each x iBring polynomial function into
Figure BSA00000518091000043
3.3 raw data is modified to (x j, Y j), Y wherein j=y j-yy j
Above-mentioned steps is that all data points are carried out data fitting, has comprised the full detail of data, therefore can simulate " trend " of data more accurately and eliminate the uneven problem of solution data baseline.This disposal route is to adopting under the less situation of data volume, at this moment all data being carried out match and can not cause the excessive problem of calculated amount.
Realization of the present invention also is: structure, the method for solving of the described segmentation cubic spline functions of step D, the segmentation cubic spline functions of structure will satisfy following three conditions: (1) s (xc i)=yc i(2) at each minizone [xc i, xc I+1], (i=0,1,2 ..., be a cubic polynomial on N-1); (3) s (x) is at [xc 0, xc N] on have the Second Order Continuous derivative; Structure, find the solution segmentation cubic spline functions s=s (x) and comprise the steps:
4.1 according to condition (1) and condition (2), at each minizone [xc i, xc I+1], (i=0,1,2 ..., N-1) structure s=s (x) is as follows:
s(x)=(1+2(x-xc i)/(x i+1-xc i))((x-xc i+1)/(xc i-xc i+1)) 2yc i
+(1+2(x-xc i+1)/(xc i-xc i+1))((x-xc i)/(xc i+1-xc i)) 2yc i+1
+(x-xc i)((x-xc i+1)/(xc i-xc i+1)) 2m i+(x-xc i+1)((x-xc i)/(xc i+1-xc i)) 2m i+1
4.2 contain unknown parameter m in the following formula i, according to condition (3), and additional boundary condition s " (xc 0)=s " (xc N)=0 obtains about m iSystem of equations:
2 m 0 + αm 1 = β 0 ( 1 - α i ) m i - 1 + 2 m i + a i m i + 1 = β i ( i = 1,2 , . . . , n - 1 ) ( 1 - α n ) m n - 1 + 2 m n + 2 m n = β n
In the formula: a 0=1, a 1=h I-1/ (h I-1+ h i), (i=1,2 ..., n-1), a n=0, β 0=3 (yc 1-yc 0)/h 0,
β i=3((1-a i)(yc i-yc i-1)/h i-1+a i(yc i+1-yc i)/h i),i=1,2,...n-1,
β n=3(yc n-yc n-1)/h n-1,h i=xc i+1-xc i,i=0,1,2,...,n-1;
Separate this system of equations and obtain parameter m iValue, with parameter x c j, yc j, m jAmong the cubic spline functions s of surface construction, promptly obtain the cubic spline functions of asking in the substitution.
For long data, the minimum point of each pulse wave cycle can reflect the baseline trend of long data well, and the minimum point that above-mentioned steps is chosen each pulse wave cycle is the difference point of cubic spline difference approach, and the effect that the deal with data baseline is uneven is very good.And because data are longer, polynomial expression often is difficult to accurately simulate the trend of data, is very easy to destroy the pulse condition information in the raw data, the phenomenon of polynomial expression substantial deviation raw data for example can occur at the data two ends, destroys raw data.And the present invention is directed to the problem that calculated amount is very big and destroy raw data, and adopt the cubic spline difference approach, efficiently solve the problem of raw data waveform distortion.
The present invention compared with prior art has the following advantages:
(1) number through the pulse wave cycle that comprises in the recognition data, the length of judgment data; Length according to data is different, adopts different disposal routes, makes treatment effect use a kind of method better than simple, and round-off error is littler; In the division of pulse wave cycle and identifying, taked accelerated method, total processing speed is improved greatly.
(2) when data volume hour; The present invention adopts the cubic polynomial fit method to handle; Owing to be that all data points are carried out data fitting; Therefore the full detail that has comprised data can simulate " trend " of data more accurately and eliminate the uneven problem of solution data baseline.And, the disposal route that the present invention is different according to the different choice of data volume, this modification method is under the less situation of data volume, to use, and does not increase calculated amount.
(3) when data volume was big, the present invention adopted the cubic spline difference approach to handle, and had avoided because data are long, and polynomial fitting method is fitting data trend and the excessive shortcoming of calculated amount well; The minimum point of choosing each pulse wave cycle is the difference point of cubic spline difference approach, can reflect the baseline trend of long data well, and the effect that the deal with data baseline is uneven is fine.
Description of drawings
Fig. 1 is a schematic flow sheet of the present invention;
Fig. 2 is the uneven pulse data synoptic diagram of baseline;
Fig. 3 is the acquired original data plot of embodiment 1;
Fig. 4 is that the present invention carries out revised data plot to Fig. 3 data;
Fig. 5 is embodiment 1 a treatment effect comparison diagram, and wherein 5 (a) are raw-data maps, and 5 (b) are the data plots after handling;
Fig. 6 is embodiment 2 input cycle data identification division figure;
Fig. 7 is embodiment 2 treatment effect comparison diagrams, and wherein 7 (a) are raw-data maps, and 7 (b) are the data plots after handling.
Embodiment
Below in conjunction with accompanying drawing to further explain of the present invention.
Embodiment 1:
The present invention is the uneven modification method of a kind of pulse wave data baseline, adopts HK2000H type pulse transducer to gather raw data, utilizes the present invention that the pulse wave data baseline of injustice is revised, and referring to Fig. 1, specifically carries out following steps:
A. import the original pulse data (x that gathers by pulse transducer j, y j); The pulse wave cycle that these data comprise is no less than 3; The pulse wave data of input comprise 5 complete pulse cycles in this example, see Fig. 3, and the baseline of these data is uneven: in preceding 800 data areas; The data baseline has the epirelief trend of arch, is unfavorable for very much the Chinese medicine pulse information that comprises in the pulse signal is further analyzed;
B. discern and divide the pulse wave cycle that comprises in the original pulse data, the division of each pulse wave cycle is a separation with the decent end in each cycle, and separation is exactly the minimum point of each pulse wave, obtains the minimum point (xc of each pulse wave in the raw data j, yc j) and number N, specifically comprise following steps:
2.1. make loop variable i=i 0, i 0=round (0.4f 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes x round, x=0.4f here 0, expression need be to 0.4f 0F in the round, this example 0=233, i 0=93;
2.2. relatively the ordinate of i data points with its before 92 data and the size of 92 data ordinates thereafter, are minimum value as if the ordinate of these data, then write down the i value, make i=i+jump then, jump=round (0.3f 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes the x round, and jump=70 in this example if the ordinate of these data is not a minimum value, then makes i=i+1;
2.3. if i<T-i 0-1=1500-93-1, then repeating step 2.2, otherwise carry out steps 2.4, the total length of the pulse data that T representes to import in the formula, T=1500 in this example;
2.4. all i values of discerning successively and writing down in the output step 2.2, these values are exactly horizontal ordinate xc corresponding to the division separation of each pulse cycle in raw data iIn this example in the step 2.2 common recognition not with write down N=5 i value, be respectively: 217,399,585,775,958}, as shown in Figure 3.Horizontal ordinate is about 20 to have located a minimum point, but because the decent terminal point that this point is not a complete pulse wave cycle, so will not discern division.
C. owing to N<7 in this example,, specifically comprise following steps so carry out data correcting method based on fitting of a polynomial:
3.1 according to raw data (x j, y j), separate about a iSystem of equations: Obtain coefficient a i, and then polynomial fitting is arranged
Figure BSA00000518091000072
The cubic polynomial that simulates in this example is: P=0.0000x 3-0.0004x 2+ 0.2267x 1+ 49.1045x 0
3.2 with raw data (x i, y i) in each x iBring polynomial function into
Figure BSA00000518091000073
Polynomial function is carried out discretize handle,
Figure BSA00000518091000074
3.3 raw data is modified to (x j, Y j), Y wherein j=y j-yy jCarry out step e;
E. obtain the pulse wave data (x of unified baseline j, Y j), with this revised pulse data as output.With revised data mapping, as shown in Figure 4.Each pulse wave cycle is basicly stable, and baseline reaches unanimity.
For the degree of stability of data baseline before and after contrast is revised better, the input and output in this example are done among Fig. 5 simultaneously.Fig. 5 (a) is the data before handling, and Fig. 5 (b) is the data after the present invention handles.Make horizontal boost line i and ii in the drawings respectively, make its with figure in the minimum point of data tangent, can get horizontal boost line i and be positioned at Fig. 5 (a) about 5 unit places more than the abscissa axis, horizontal boost line ii is positioned at Fig. 5 (b) about 60 unit places below the abscissa axis.Each division points of comparison pulse ripple is apart from the distance of boost line; The division points ordinate of finding pulse wave among Fig. 5 (a) is apart from the most about 30 units of horizontal boost line i; Be positioned at regional III; And the division points ordinate of pulse wave is positioned at regional IV apart from the most about 8 units of horizontal boost line among revised Fig. 5 (b).Through comparative descriptions, the baseline modification method that the present invention is based on fitting of a polynomial is very effective to the baseline problem that solves pulse data.
Embodiment 2:
The modification method of pulse wave data baseline injustice wherein uses segmentation cubic spline interpolation method to the bigger situation of data volume with embodiment 1.
Pulse wave baseline modification method based on segmentation cubic spline interpolation method is following:
A. one section pulse wave data uneven than long baseline of input in this example comprise 33 cycles;
B. with identification in the instance 1 and divide the method for the pulse wave cycle that comprises in the original pulse data, obtain this segment data and comprise N=33 pulse wave cycle altogether, and the minimum point (xc of each pulse wave in the raw data i, yc i), (i=1,2 ..., 21).Identification is as shown in Figure 6 with results;
C. because of N >=7, so skips steps C directly carries out step D;
D. because N>=7 adopt segmentation cubic spline interpolation method that data are revised: with the minimum point (xc of each pulse wave i, yc i) be the difference point of cubic spline interpolation, the structure cubic spline functions:
s(x)=(1+2(x-xc i)/(x i+1-xc i))((x-xc i+1)/(xc i-xc i+1)) 2yc i
+(1+2(x-xc i+1)/(xc i-xc i+1))((x-xc i)/(xc i+1-xc i)) 2yc i+1
+(x-xc i)((x-xc i+1)/(xc i-xc i+1)) 2m i+(x-xc i+1)((x-xc i)/(xc i+1-xc i)) 2m i+1
(i=1,2,...,20)
Separate about unknown parameter m iSystem of equations:
2 m 0 + αm 1 = β 0 ( 1 - α i ) m i - 1 + 2 m i + a i m i + 1 = β i ( i = 1,2 , . . . , n - 1 ) ( 1 - α n ) m n - 1 + 2 m n + 2 m n = β n
In the formula: a 0=1, a i=h I-1/ (h I-1+ h i), (i=1,2 ..., n-1), a n=0, β 0=3 (yc 1-yc 0)/h 0,
β i=3((1-a i)(yc i-yc i-1)/h i-1+a i(yc i+1-yc i)/h i),i=1,2,...n-1,
β n=3(yc n-yc n-1)/h n-1,h i=xc i+1-xc i,i=0,1,2,...,n-1;
Separate this system of equations and obtain parameter m iValue, with parameter x c i, yc i, m iAmong the cubic spline functions s of surface construction, promptly obtain the cubic spline functions s=s that asks (x) in the substitution; With raw data (x i, y i) in each x iBring into and carry out the processing of function discretize among the interpolating function s=s (x), get yy i=s (x i); Make Y i=y i-yy i, obtain revised data and be: (x i, Y i);
E. will obtain the pulse wave data (x of unified baseline j, Y j), with this revised pulse data as output.
For the degree of stability of data baseline before and after contrast is revised better, the input and output in this example are done among Fig. 7 simultaneously.Fig. 7 (a) is the data before handling, and Fig. 7 (b) is the data after the present invention handles, and its data baseline obviously is improved, and is tending towards unified.It is thus clear that the baseline correction that the present invention is based on segmentation cubic spline interpolation method is very effective to the baseline problem that solves pulse data under the big data quantity situation.And, adopt the cubic spline difference approach, efficiently solve the problem of raw data waveform distortion, protected the pulse condition information in the raw data to be without prejudice.
Embodiment 3:
The modification method of pulse wave data baseline injustice wherein uses the cubic polynomial approximating method to the less situation of data volume with embodiment 1.
The original pulse wave data of importing in this example are very short, have only N=3 pulse wave cycle, and its baseline has the trend to the upper right side inclination.Utilize baseline modification method of the present invention, obtain the cubic fit polynomial expression and be: P=0.0000x 3+ 0.0001x 2+ 0.0231x 1+ 53.3214x 0, after the discretize, data are revised.Use the present invention very good to the correction effect of these data.The explanation of this example, to the baseline correction than short data, the present invention is practical, effective, quick.
Embodiment 4:
The modification method of pulse wave data baseline injustice wherein uses segmentation cubic spline interpolation method to the bigger situation of data volume with embodiment 1.
The original pulse wave data of importing in this example have N=7 pulse wave cycle, and its length is the parameter threshold point that the present invention selects modification method just, and the baseline of these data is shaken more serious up and down.Utilize baseline modification method of the present invention, adopt segmentation cubic spline interpolation method, obtain cubic spline functions, after the discretize, data are revised.Use the present invention very good to the correction effect of these data.The explanation of this example, the present invention is effectively same to the baseline correction of long data and short data.

Claims (4)

1. the uneven modification method of a pulse wave data baseline, it is characterized in that: the pulse wave data correction of uneven baseline comprises the steps:
A. import the original pulse data (x that gathers by pulse transducer j, y j), the pulse wave cycle that these data comprise is no less than 3;
B. discern and divide the pulse wave cycle that comprises in the original pulse data, the division of each pulse wave cycle is a separation with the decent end in each cycle, and separation is exactly the minimum point of each pulse wave, obtains the minimum point (xc of each pulse wave in the raw data j, yc j) and number N;
C. if N<7, then carry out data correction based on fitting of a polynomial: according to least square method to raw data (x j, y j) carry out fitting of a polynomial, obtain polynomial function
Figure FSA00000518090900011
In each fitting coefficient a i, x is the polynomial expression independent variable in the formula, and P is a dependent variable, and n is the degree of polynomial, with x jBring polynomial function into
Figure FSA00000518090900012
Carry out the function discretize,
Figure FSA00000518090900013
Make Y j=y j-yy j, raw data is modified to (x j, Y j), carry out step e then; If step D is then carried out in N>=7;
D. if the data correction based on the segmentation cubic spline interpolation is then carried out: with (the xc that discerns among the step B in N>=7 j, yc j) be interpolation point, construct and find the solution segmentation cubic spline functions s=s (x), to raw data (x j, y j), with x jBring among the segmentation cubic spline functions s=s (x) and carry out the function discretize, get yy j=s (x j), make Y j=y j-yy j, raw data is modified to (x j, Y j), carry out step e;
E. obtain the pulse wave data (x of unified baseline j, Y j), with this revised pulse data as output.
2. the modification method that pulse wave data baseline according to claim 1 is uneven, it is characterized in that: the described identification of step B is also divided the pulse wave cycle that comprises in the original pulse data, comprises the steps:
2.1. make loop variable i=i 0, i 0=round (0.4f 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes x round, x=0.4f here 0, expression need be to 0.4f 0Round;
2.2. compare the ordinate and the (i before it of i data points 0-1) individual data and (i thereafter 0-1) size of individual data ordinate, if the ordinate of these data is minimum value, then record i value at this moment makes i=i+jump, jump=round (0.3f then 0), f in the formula 0Be the SF of pulse transducer, function round (x) representes the x round, if the ordinate of these data is not a minimum value, then makes i=i+1;
2.3. if i<T-i 0-1, then repeating step 2.2, otherwise carry out steps 2.4, and T representes the total number in original Pulse Rate strong point imported in the formula;
2.4. all i values of discerning successively and writing down in the output step 2.2, these values are exactly horizontal ordinate xc corresponding to the division separation of each pulse cycle in raw data i
3. the modification method that pulse wave data baseline according to claim 2 is uneven, it is characterized in that: the described data correcting method based on fitting of a polynomial of step C comprises the steps:
3.1 according to raw data (x j, y j), separate about a iSystem of equations:
Figure FSA00000518090900021
Obtain coefficient a i, and then polynomial fitting is arranged P = Σ i = 0 n a i x i ;
3.2 with raw data (x i, y i) in each x iBring polynomial function into
Figure FSA00000518090900023
Figure FSA00000518090900024
3.3 raw data is modified to (x j, Y j), Y wherein j=y j-yy j
4. pulse wave data baseline disposal route according to claim 2 is characterized in that: structure, the method for solving of the described segmentation cubic spline functions of step D, this function requires to satisfy following three conditions: (1) s (xc i)=yc i(2) at each minizone [xc i, xc I+1], (i=0,1,2 ..., be a cubic polynomial on N-1); (3) s (x) is at [xc 0, xc N] on have the Second Order Continuous derivative; Ask the segmentation cubic spline functions to comprise the steps:
4.1 according to condition (1) and condition (2), at each minizone [xc i, xc I+1], (i=0,1,2 ..., N-1) structure s=s (x) is as follows:
s(x)=(1+2(x-xc i)/(x i+1-xc i))((x-xc i+1)/(xc i-xc i+1)) 2yc i
+(1+2(x-xc i+1)/(xc i-xc i+1))((x-xc i)/(xc i+1-xc i)) 2yc i+1
+(x-xc i)((x-xc i+1)/(xc i-xc i+1)) 2m i+(x-xc i+1)((x-xc i)/(xc i+1-xc i)) 2m i+1
4.2 contain unknown parameter m in the following formula i, according to condition (3), and additional boundary condition s " (xc 0)=s " (xc N)=0 obtains about m iSystem of equations:
2 m 0 + αm 1 = β 0 ( 1 - α i ) m i - 1 + 2 m i + a i m i + 1 = β i ( i = 1,2 , . . . , n - 1 ) ( 1 - α n ) m n - 1 + 2 m n + 2 m n = β n
In the formula: a 0=1, a i=h I-1/ (h I-1+ h i), (i=1,2 ..., n-1), a n=0, β 0=3 (yc 1-yc 0)/h 0,
β i=3((1-a i)(yc i-yc i-1)/h i-1+a i(yc i+1-yc i)/h i),i=1,2,...n-1,
β n=3(yc n-yc n-1)/h n-1,h i=xc i+1-xc i,i=0,1,2,...,n-1;
Separate this system of equations and obtain parameter m iValue, with parameter x c j, yc j, m jAmong the cubic spline functions s of surface construction, promptly obtain the cubic spline functions s=s that asks (x) in the substitution.
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