CN106452389B - Based on index recycle window temporal modulation filter design method and filter - Google Patents
Based on index recycle window temporal modulation filter design method and filter Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0211—Frequency selective networks using specific transformation algorithms, e.g. WALSH functions, Fermat transforms, Mersenne transforms, polynomial transforms, Hilbert transforms
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H2017/0072—Theoretical filter design
Abstract
The invention discloses one kind being based on index recycle window temporal modulation filter design method and filter, is related to wave filter technology field.The filter of the method design has the temporal modulation function of extremely simple exponential function form, in order to further increase realizability, for the signal after frequency domain modulation, temporal modulation function is multiplied it by into the process integrated again and is equivalent to an exponential filter, it is easier to be realized.
Description
Technical field
The present invention relates to wave filter technology fields, more particularly to a kind of index recycle window temporal modulation filter that is based on to design
Method and filter.
Background technology
Finite time length narrow pulse signal owes the hot spot that Nyquist sampling techniques are recent domestic research, in thunder
It reaches, the various fields such as ultrasonic listening all have a wide range of applications.For this kind of signal, the Ewa Matusiak of Israel's science and engineering
With Yonina C.Eldar according to Gabor sampling principles, propose that the narrow pulse signal based on Gabor frames owes Nyquist samplings
With the theoretical model of reconstruct, sample rate can be reduced to the one of the duration point of transient signal, and utilize compressed sensing
(Compressed Sensing, CS) is theoretical to reduce ampling channel number, has important theory significance.But its sampling system
It is poor to design engineering.The window function used during modulation to signal adding window in analog domain is complicated, and cost of implementation is high
High and high to clock request, the form that can not pass through simple filter in similar MWC is realized.The calculation matrix of uncertainty exists
It is difficult to be engineered in practical application, especially be realized under the conditions of multichannel more difficult.
Invention content
Technical problem to be solved by the invention is to provide one kind being based on index recycle window temporal modulation filter design side
Method and filter, the temporal modulation function with extremely simple exponential function form are realized and are easy.
In order to solve the above technical problems, the technical solution used in the present invention is：One kind being based on index recycle window time domain tune
Filter design method processed, it is characterised in that include the following steps：
First, by the time-domain of multipulse signal x (t) from t ∈ [-T/2,T/2]It is extended to t ∈ [0,T], multipulse signal
Single pulse h (t) maximum widths of x (t) are W, and in time domain compact schemes, and pulse maximum number is Np, wherein WNp< < T, letter
Number x (t) is real function, and the mathematic(al) representation of model is
Wherein
Signal x (t) enter a channel (j, m), first with frequency modulation(PFM) function wj(t) it is multiplied, recycles filter χm
(t) it is filtered, signal sampling is completed in the final output for acquiring the t=τ moment；
Signal x (t) is synchronous to enter JM channel, in a channel (j, m), signal x (t) first with function qj,m(t)=
wj(t)sm(t) it is multiplied, integrator is recycled to complete integral, wherein 0≤j≤J-1,0≤m≤M-1, andFunction qj,m
(t) according to Gabor framesIt is designed, window function g (t) is in Shi Jianyu [0,Wg]Upper compact schemes, and itsThis
Matter bandwidth is [-Bg/2,Bg/2]；Enable K1、K2And L0MeetWithIts
In, B and Ω are respectively the essential bandwidth of multipulse signal x (t) and index regeneration window function g (t), and N indicates index recycle window letter
The smooth exponent number of number g (t)；
Then qj,m(t) expression formula is
qj,m(t)=wj(t)sm(t) (2)
Wherein
In formula (3), wj(t) it is frequency domain modulation function, sm(t) it is temporal modulation function；Signal x (t) is a by (j, m)
It is sampled behind channel, the measured value on each channel is indicated by formula (4)：
Measured value y is obtained by sampling systemj,mAfterwards, according to the d in modulation functionjlAnd cmkParameter information solves
Gabor coefficients zk,l, formula (5) is recycled to synthesize original signal x (t)；
The improved Gabor frame sampling systems that window function is regenerated based on index, if its window function is g (t)=βα(tN/
Wg), T-F-grid is (μ Wg,1/Wg), responses of the x (t) in a channel (j, m) is through wj(t) signal modulated passes through filtering
Device χm(t) in the timeThe transient response at place, χm(t) expression formula is
In sampling system, sampling instant isχm(t) it is to convert m channel inner product link of system jth to
After convolution link, sm(t) filter function corresponding to, such frame window function βα(t) design has been converted to filter χm
(t) the problem of designing；To χm(t) it carries out Laplace transform and obtains frequency response
Enable αm=α0+ i λ (m), wherein m=1,2 ... M knows Re[ by Laplace transform convergent requirement;s]>-α0；In order to
Simplify Xm(s), α is taken0=Wg/WN；Since signal x (t) pulsewidths are much smaller than total duration, i.e. T > > W, if W >=Wg, then meetThe s in m channel of system jth in this waym(t) single order Butterworth is translated into
Filter
In addition, g (t)=βα(tN/Wg) it is N number of first order exponential spline function βαm(tN/Wg) convolution, in order to ensure window letter
Number g (t) is the real function of compact schemes, for m=1 ..., M, chooses sequence α and disclosure satisfy that
λ (m)+λ (M+1-m)=0 (9)
According to the design of improved sampling system model, the index recycle window in m-th of channel is weighted integral and constitutes
Filter function such as formula (8), this is a single complex poles filter function, be cannot achieve in practice in engineering；Cause
This, considers to merge with two channels for being conjugated symmetrical pole, to ensure window function g (t)=βα(t) it is real function, α
=(α1,α2,...,αN) in element be made of conjugate pair；Assuming that total port number is M, and M=N, respectively to m and M+
The channels 1-m, which mutually sum it up, to be subtracted each other to obtain
In order to avoid repeating, enable 0≤m≤(M+1)/2, then all elements indicated by m and M+1-m may make up set 1,
2,…,M}；
On this basis, two channels can be obtained first in sampling instant t=TsResponse y 'p(m)(Ts) and y 'p(M+1-m)
(Ts), two channel response y of actual needs are derived further according to theory analysism(Ts) and yM+1-m(Ts)；Then CS is utilized to reconstruct
Algorithm carries out subspace detection；The problem of needing exist for two most criticals completed is to obtain t=TsSampling instant response results
Between mapping relations, if real number be responsive to plural number response operator beOperator needs to ensure to meet
It enables
Then
It enablesIt brings formula (13) into (10) mathematical model of filter can be obtained and be
It is designed based on index recycle window temporal modulation filter according to formula (14).
The invention also discloses one kind being based on index recycle window temporal modulation filter, it is characterised in that the filter packet
Include filter X 'p(m)(s) and filter X 'p(M+1-m)(s), the filter X 'p(m)(s) include operational amplifier U1, resistance Rm1
One end be the X 'p(m)(s) other end of the signal input part of filter, resistance Rm1 is divided into two-way, and the first via is through capacitance
Cm1 is connect with the output end of operational amplifier U1, and the second tunnel is divided into after resistance R ' m2 as two-way, the first via and operational amplifier
The in-phase input end of U1 connects, and the second tunnel is grounded after capacitance Cm2, resistance R ' m3 successively；A termination operation amplifier of resistance R ' a
The other end of the output end of device U1, resistance R ' a is grounded after resistance R ' b, and the node of resistance R ' a and resistance R ' b connects operation amplifier
The inverting input of device U1；
The filter X 'p(M+1-m)(s) include operational amplifier U2, one end of another resistance Rm1 is described
X′p(M+1-m)(s) other end of the signal input part of filter, another resistance Rm1 is divided into two-way, and the first via is through another capacitance
Cm1 is connect with the output end of operational amplifier U2, and the second tunnel is divided into after resistance Rm2 as two-way, the first via and operational amplifier
The in-phase input end of U2 connects, and the second tunnel is grounded through another capacitance Cm2；The output of a termination operational amplifier U2 of resistance Ra
End, the other end of resistance Ra are grounded after resistance Rb, and the node of resistance Ra and resistance Rb connects the anti-phase input of operational amplifier U2
End.
Further technical solution is：
If enabling KR=1+Rb/Ra, then filter X 'p(m)(s) and filter X 'p(M+1-m)(s) mathematical model X 'p(m)(s) and
X′p(M+1-m)(s) it is respectively
Enable Rb=0, then by RaIt disconnects, i.e. Ra=∞, then KR=1；It enablesThenThen formula (15) simplifies
For
Then in order to ensure that formula (16) denominator is identical, need to meet
Convolution (14), it is known that when determining the numerical value of resistance and capacitance, it is also necessary to meet
In addition, in order to which the gain and formula (14) that ensure filter are identical, need respectively in X 'p(m)(s) and X 'p(M+1-m)(s)
Increase an amplifying circuit before two filters, the gain of the two circuits is respectively
It is using advantageous effect caused by above-mentioned technical proposal：The filter of the method design has extremely simple
Exponential function form temporal modulation function, in order to further increase realizability, for the signal after frequency domain modulation, by when
Domain modulation function multiplies it by the process integrated again and is equivalent to an exponential filter, it is easier to realize.
Description of the drawings
Fig. 1 is index recycle window Gabor sampling system filter construction models；
Fig. 2 is median filter of embodiment of the present invention X 'p(m)(s) schematic diagram；
Fig. 3 is median filter of embodiment of the present invention X 'p(M+1-m)(s) schematic diagram；
Fig. 4 is median filter of embodiment of the present invention X 'p(26)(s) amplitude-versus-frequency curve figure；
Fig. 5 is median filter of embodiment of the present invention X 'p(26)(s) step response curve figure；
Fig. 6 is median filter of embodiment of the present invention Xp(26)(s) amplitude-versus-frequency curve figure；
Fig. 7 is median filter of embodiment of the present invention Xp(26)(s) step response curve figure.
Specific implementation mode
With reference to the attached drawing in the embodiment of the present invention, technical solution in the embodiment of the present invention carries out clear, complete
Ground describes, it is clear that described embodiment is only a part of the embodiment of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Many details are elaborated in the following description to facilitate a thorough understanding of the present invention, still the present invention can be with
Implemented different from other manner described here using other, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by following public specific embodiment.
The invention discloses one kind being based on index recycle window temporal modulation filter design method, includes the following steps：
First, by the time-domain of more arteries and veins signal x (t) from t ∈ [-T/2,T/2]It is extended to t ∈ [0,T], multipulse signal x
(t) single pulse h (t) maximum widths are W, and in time domain compact schemes, and pulse maximum number is Np, wherein WNp< < T, signal
X (t) is real function, and the mathematic(al) representation of model is
Wherein
Improve sampling system structure as shown in Figure 1, signal x (t) enter a channel (j, m), first with frequency modulation(PFM) letter
Number wj(t) it is multiplied, recycles filter χm(t) it is filtered, signal sampling is completed in the final output for acquiring the t=τ moment；
Signal x (t) is synchronous to enter JM channel, in a channel (j, m), signal x (t) first with function qj,m(t)=
wj(t)sm(t) it is multiplied, integrator is recycled to complete integral, wherein 0≤j≤J-1,0≤m≤M-1, andFunction qj,m
(t) according to Gabor framesIt is designed, window function g (t) is in Shi Jianyu [0,Wg]Upper compact schemes, and itsThis
Matter bandwidth is [-Bg/2,Bg/2]；Enable K1、K2And L0MeetWith
Wherein, B and Ω is respectively the essential bandwidth of multipulse signal x (t) and index regeneration window function g (t), and N indicates index recycle window
The smooth exponent number of function g (t)；
Then qj,m(t) expression formula is
qj,m(t)=wj(t)sm(t) (2)
Wherein
In formula (3), wj(t) it is frequency domain modulation function, sm(t) it is temporal modulation function；Signal x (t) is a by (j, m)
It is sampled behind channel, the measured value on each channel is indicated by formula (4)：
Measured value y is obtained by sampling systemj,mAfterwards, according to the d in modulation functionjlAnd cmkParameter information solves
Gabor coefficients zk,l, formula (5) is recycled to synthesize original signal x (t)；
The improved Gabor frame sampling systems that window function is regenerated based on index, if its window function is g (t)=βα(tN/
Wg), T-F-grid is (μ Wg,1/Wg), responses of the x (t) in a channel (j, m) is through wj(t) signal modulated passes through filtering
Device χm(t) in the timeThe transient response at place, χm(t) expression formula is
In sampling system, sampling instant isχm(t) it is to convert m channel inner product link of system jth to
After convolution link, sm(t) filter function corresponding to, such frame window function βα(t) design has been converted to filter χm
(t) the problem of designing；To χm(t) it carries out Laplace transform and obtains frequency response
Enable αm=α0+ i λ (m), wherein m=1,2 ... M knows Re[ by Laplace transform convergent requirement;s]>-α0；In order to
Simplify Xm(s), α is taken0=Wg/WN；Since signal x (t) pulsewidths are much smaller than total duration, i.e. T > > W, if W >=Wg, then meetThe s in m channel of system jth in this waym(t) single order Butterworth is translated into
Filter
In addition, g (t)=βα(tN/Wg) it is N number of first order exponential spline functionConvolution, in order to ensure window
Function g (t) is the real function of compact schemes, for m=1 ..., M, chooses sequence α and disclosure satisfy that
λ (m)+λ (M+1-m)=0 (9)
According to the design of improved sampling system model, the index recycle window in m-th of channel is weighted integral and constitutes
Filter function such as formula (8), this is a single complex poles filter function, be cannot achieve in practice in engineering；Cause
This, considers to merge with two channels for being conjugated symmetrical pole, to ensure window function g (t)=βα(t) it is real function, α
=(α1,α2,...,αN) in element be made of conjugate pair；Assuming that total port number is M, and M=N, respectively to m and M+
The channels 1-m, which mutually sum it up, to be subtracted each other to obtain
In order to avoid repeating, m≤(M+1)/2 is enabled；Exponential sequence set { 1,2 ..., M } can be collectively formed by m and M+1-m；
On this basis, two channels can be obtained first in sampling instant t=TsResponse y 'p(m)(Ts) and y 'p(M+1-m)
(Ts), two channel response y of actual needs are derived further according to theory analysism(Ts) and yM+1-m(Ts)；Then CS is utilized to reconstruct
Algorithm carries out subspace detection；The problem of needing exist for two most criticals completed is to obtain t=TsSampling instant response results
Between mapping relations, if real number be responsive to plural number response operator beOperator needs to ensure to meet
It enables
Then
It enablesIt brings formula (13) into (10) mathematical model of filter can be obtained and be
It is designed based on index recycle window temporal modulation filter according to formula (14).
The invention also discloses one kind being based on index recycle window temporal modulation filter, and it includes filter to state filter
X′p(m)(s) and filter X 'p(M+1-m)(s), filter X 'p(m)(s) and X 'p(M+1-m)(s) design can be considered using passive filter
Wave device or active filter.Due to that volume may be needed larger and accurate inductance using passive filter, when adjustment, is excessively numb
Tired, therefore the present invention considers to use Sallen-Key filters, this filter construction is simple, and only need an amplifier and
Less capacitance and resistance can be achieved with, therefore the present invention determines to use Sallen-Key filters.Low pass Sallen-Key filters
Wave device schematic diagram is as Figure 2-3.
If enabling KR=1+Rb/Ra, then
If enabling Rb=0, then by RaIt disconnects, i.e. Ra=∞, then KR=1；It enablesThenThen formula (15)
It is reduced to
Then in order to ensure that formula (16) denominator is identical, need to meet
Convolution (14), it is known that when determining the numerical value of resistance and capacitance, it is also necessary to meet
In addition, in order to which the gain and formula (14) that ensure filter are identical, need respectively in X 'p(m)(s) and X 'p(M+1-m)(s)
Increase an amplifying circuit before two filters.The gain of the two circuits is respectively
The selection of filter circuit parameter：
During carrying out theoretical model analysis to filter, for ease of calculation, α is enabled0=Wg/WN.But in practical system
In design process of uniting, it is contemplated that sampling system can utilize switch to block the realization of filter receptance function, therefore, can be by α0
Be set as one more level off to 0 value so that at sampling time t=τ step response value it is as big as possible, the present invention enables α0=
0.01Wg/N.Sampling system median filter design success or not three key parameters be：Indicial response decay factor Am, index
Respond modulation factor BmWith system bandwidth BW.
Filter receptance function in formula (16) can be uniformly indicated with formula (20)
This is a second-order system function, and the resonance point of function is
Filter step response is the periodic response of exponential damping, period Bm/ 2 π, work as f0And Bm/ 2 π are very accurate
When, it is ensured that AmAccuracy.In addition, system bandwidth wants sufficiently wide, it just can guarantee narrow pulse signal during sampling
Be not in that information is lost.
In practice, filter is devised for the multipulse signal of the finite time length of length T=20ms.Setting letter
The maximum width comprising burst pulse is the Gaussain pulses of W=0.5ms in number, and bandwidth can be BW with "ball-park" estimateP=
1/W=2kHz, it is therefore desirable at least meet BW >=BWP。
According to formula (17) and formula (18), Rm1、Rm2、Cm1And Cm2Specific calculation expression be
Take Cm1=10 μ F, emulate by PSpice, it is known that as M+1-2m >=26, meet filter design bandwidth
Requirement, i.e. BW >=BWP。
Here the design of the filter as M+1-2m >=26 is analyzed first.At this point, Cm2=33.3pF, Rm1=15k Ω, Rm2
=3k Ω.Filter X 'p(26)(s) amplitude-versus-frequency curve is as shown in Figure 4.
Under the conditions of this parameter setting, the resonance point f of filter0=1.3007kHz, filter X 'p(26)(s) emulation obtains
Resonance point beError is 0.0384%, therefore can ensure AmAnd BmAccuracy.Bandwidth
ForMeet design requirement.
Filter X 'p(26)(s) step response curve is as shown in figure 5, for convenience and Xp(26)(s) response curve into
Row comparison, data are normalized using circuit.The angular frequency that response curve can be obtained by Fig. 5 is 7.9294 × 103, and B26=
8.1681×103, error 2.92%.This error is less than the deviation between two neighboring channel angular frequency, it is contemplated that in signal subspace
Redundancy, the response curve of filter existing for calculation matrix C itself meet design requirement during space exploration.
It correspondingly, can be in the hope of filter X according to formula (17)p(26)(s) capacitance and resistance value, amplitude-versus-frequency curve is such as
Shown in Fig. 6.
As seen from the figure, filter Xp(26)(s) bandwidthIt is far longer than signal bandwidth BWP.This is because system
Function Xp(26)(s) it is equivalent in X 'p(26)(s) zero is increased on basis, has delayed the amplitude of resonance point with frequency
Decaying.It is compared with Fig. 7, resonant frequencySubstantially with filter X 'p(26)(s) quite.Filter Xp(26)
(s) step response curve is as shown in Figure 7.
As shown in Figure 7, the angular frequency of response curve is 8.3472 × 103, and B26=8.1681 × 103, error 2.19%,
Meet design requirement.It is compared with Fig. 5, response curve phase shift π/4, it was demonstrated that the response of two filters can by formula (13)
To synthesize corresponding complex exponential coefficient.
The design of filter under the conditions of M+1-2m=26 is analyzed above, and its fundamental characteristics is emulated.Due to
Such filter needs are designed in pairs, in order to ensure M+1-2m >=26, window function Smoothness Index are needed to meet N >=52.
The channel of exclusion m≤25 is needed when building sampling system using low pass Sallen-Key filters, therefore actual port number is answered
Should be M=N-50.N is bigger and port number is more, and sample reconstruction effect is better, so being subjected to complexity in sampling system
Under, selection N as big as possible.
The method has the temporal modulation function of extremely simple exponential function form, achievable in order to further increase
Property, for the signal after frequency domain modulation, temporal modulation function is multiplied it by into the process integrated again and is equivalent to an index
Filter, it is easier to realize.
Claims (3)
1. one kind being based on index recycle window temporal modulation filter design method, it is characterised in that include the following steps：
First, by the time-domain of more arteries and veins signal x (t) from t ∈ [-T/2,T/2]It is extended to t ∈ [0,T], multipulse signal x's (t)
Single pulse h (t) maximum widths are W, and in time domain compact schemes, and pulse maximum number is Np, wherein WNp< < T, signal x (t)
Mathematic(al) representation for real function, model is
Wherein
Signal x (t) enter a channel (j, m), first with frequency modulation(PFM) function wj(t) it is multiplied, recycles filter χm(t) into
Signal sampling is completed in row filtering, the final output for acquiring the t=τ moment；
Signal x (t) is synchronous to enter JM channel, in a channel (j, m), signal x (t) first with function qj,m(t)=wj(t)
sm(t) it is multiplied, integrator is recycled to complete integral, wherein 0≤j≤J-1,0≤m≤M-1, andFunction qj,m(t) root
According to Gabor framesIt is designed, window function g (t) is in Shi Jianyu [0,Wg]Upper compact schemes, and its ∈ΩEssential band
Width width [-Bg/2,Bg/2]；Enable K1、K2And L0MeetWith
Wherein, B is the essential bandwidth of multipulse signal x (t), and Ω is the essential bandwidth that index regenerates window function g (t), and N indicates index again
The smooth exponent number of raw window function g (t)；
Then qj,m(t) expression formula is
qj,m(t)=wj(t)sm(t) (2)
Wherein
In formula (3), wj(t) it is frequency domain modulation function, sm(t) it is temporal modulation function；Signal x (t) passes through a channel (j, m)
After sampled, the measured value on each channel pass through formula (4) indicate：
Measured value y is obtained by sampling systemj,mAfterwards, according to the d in modulation functionjlAnd cmkParameter information solves Gabor coefficients
zk,l, formula (5) is recycled to synthesize original signal x (t)；
The improved Gabor frame sampling systems that window function is regenerated based on index, if its window function is g (t)=βα(tN/Wg), when
Frequency grid is (μ Wg,1/Wg), responses of the x (t) in a channel (j, m) is through wj(t) signal modulated passes through filter χm(t)
In the timeThe transient response at place, χm(t) expression formula is
In sampling system, sampling instant isχm(t) it is to convert m channel inner product link of system jth to convolution
After link, sm(t) filter function corresponding to, such frame window function βα(t) design has been converted to filter χm(t)
The problem of design；To χm(t) it carries out Laplace transform and obtains frequency response
Enable αm=α0+ i λ (m), wherein m=1,2 ... M knows Re[ by Laplace transform convergent requirement;s]>-α0；In order to simplify Xm
(s), α is taken0=Wg/WN；Since signal x (t) pulsewidths are much smaller than total duration, i.e. T > > W, if W >=Wg, then meetThe s in m channel of system jth in this waym(t) single order Butterworth is translated into
Filter
In addition, g (t)=βα(tN/Wg) it is N number of first order exponential spline functionConvolution, in order to ensure window function g
(t) it is the real function of compact schemes, for m=1 ..., M chooses sequence α and disclosure satisfy that
λ (m)+λ (M+1-m)=0 (9)
According to the design of improved sampling system model, the index recycle window in m-th of channel is weighted the filter that integral is constituted
Wave device function such as formula (8), this is a single complex poles filter function, be cannot achieve in practice in engineering；Therefore, it examines
Considering will merge with two channels for being conjugated symmetrical pole, to ensure window function g (t)=βα(t) it is real function, α=(α1,
α2,…,αN) in element be made of conjugate pair；Assuming that total port number is M, and M=N, respectively to m and the channels M+1-m
Mutually adduction subtracts each other to obtain
In order to avoid repeating, m≤(M+1)/2 is enabled；Exponential sequence set { 1,2 ..., M } can be collectively formed by m and M+1-m；
On this basis, two channels can be obtained first in sampling instant t=TsResponse y 'p(m)(Ts) and y 'p(M+1-m)(Ts), then
Two channel response y of actual needs are derived according to theory analysism(Ts) and yM+1-m(Ts)；Then utilize CS restructing algorithms into
Row subspace detects；The problem of needing exist for two most criticals completed is to obtain t=TsBetween sampling instant response results
Mapping relations, if the operator that real number is responsive to plural number response isOperator needs to ensure to meet
It enables
Then
It enablesIt brings formula (13) into (10) mathematical model of filter can be obtained and be
It is designed based on index recycle window temporal modulation filter according to formula (14).
2. it is a kind of using it is described in claim 1 based on index recycle window temporal modulation filter design method manufacture index again
Raw window temporal modulation filter, it is characterised in that the filter includes filter X 'p(m)(s) and filter X 'p(M+1-m)(s),
The filter X 'p(m)(s) include operational amplifier U1, one end of resistance Rm1 is the X 'p(m)(s) the signal input of filter
End, the other end of resistance Rm1 are divided into two-way, and the first via is connect through capacitance Cm1 with the output end of operational amplifier U1, the second road warp
It is divided into after resistance R ' m2 as two-way, the first via is connect with the in-phase input end of operational amplifier U1, and the second tunnel is successively through capacitance
It is grounded after Cm2, resistance R ' m3；The output end of a termination operational amplifier U1 of resistance R ' a, the other end of resistance R ' a is through resistance
It is grounded after R ' b, the node of resistance R ' a and resistance R ' b connects the inverting input of operational amplifier U1；
The filter X 'p(M+1-m)(s) include operational amplifier U2, one end of another resistance Rm1 is the X 'p(M+1-m)(s)
The other end of the signal input part of filter, another resistance Rm1 is divided into two-way, and the first via is through another capacitance Cm1 and operation
The output end of amplifier U2 connects, and the second tunnel is divided into after resistance Rm2 as two-way, and the first via is same mutually defeated with operational amplifier U2's
Enter end connection, the second tunnel is grounded through another capacitance Cm2；The output end of a termination operational amplifier U2 of resistance Ra, resistance Ra
The other end be grounded after resistance Rb, the node of resistance Ra and resistance Rb connect the inverting input of operational amplifier U2.
3. being based on index recycle window temporal modulation filter as claimed in claim 2, it is characterised in that：
If enabling KR=1+Rb/Ra, then filter X 'p(m)(s) and filter X 'p(M+1-m)(s) mathematical model X 'p(m)(s) and
X′p(M+1-m)(s) it is respectively
Enable Rb=0, then by RaIt disconnects, i.e. Ra=∞, then KR=1；It enablesThenThen formula (15) is reduced to
Then in order to ensure that formula (16) denominator is identical, need to meet
Convolution (14), it is known that when determining the numerical value of resistance and capacitance, it is also necessary to meet
In addition, in order to which the gain and formula (14) that ensure filter are identical, need respectively in X 'p(m)(s) and X 'p(M+1-m)(s) two
Increase an amplifying circuit before filter, the gain of the two circuits is respectively
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