CN107026650A - A kind of simulation low-pass filter, analog information converter and filtering method - Google Patents
A kind of simulation low-pass filter, analog information converter and filtering method Download PDFInfo
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Abstract
The invention discloses the simulation low-pass filter applied to AIC, analog information converter and filtering method.Simulation low-pass filter includes adder unit, state conversion unit, the first delay cell and at least one second delay cell;Adder unit is used to the mixed frequency signal of reception and the Signal averaging from state conversion unit obtaining composite signal;First delay cell is used for the delay that the unit interval is carried out to composite signal;Second delay cell is used for the delay that the unit interval is carried out to the signal from state conversion unit;State conversion unit is used to handle the signal weighting from the first delay cell and the second delay cell using loop cycle matrix, and corresponds to input respectively to adder and the second delay cell;The parameter of loop cycle matrix meets the incoherent condition of any two row of calculation matrix;One of them in first delay cell or at least one second delay cell, is additionally operable to being input to the signal after delay into the sampler being connected with simulation low-pass filter.
Description
Technical field
The present invention relates to compressed sensing field, more particularly to a kind of simulation low-pass filter, analog information converter with
And filtering method.
Background technology
It is minimum in order to ensure undistorted recovery primary signal for a broadband signal according to nyquist sampling theorem
Sampling rate needs to be more than twice of highest frequency in signal.That is, the highest frequency of signal is higher, to minimum sampling speed
The requirement of rate is also higher, develop higher sampling rate analog-digital converter (Analog-to-Digital Convertor,
ADC difficulty) is also increasing.
In order to solve this problem, scholars have found, in many practical applications, such as radar, sonar, medical detecting system
Be Deng, the information rate that signal is carried it is limited, i.e., signal have it is openness, if letter can be carried having substantially no effect on signal
On the premise of breath, it will be compressed with openness signal so that the highest frequency of signal is far below primary signal after compression
Highest frequency, can thus reduce the requirement to ADC sampling rate.After sampled signal is obtained, it is possible to use this is adopted
The information that sample signal is carried recreates primary signal, to meet the demand using primary signal.Compressed sensing
(Compressive Sensing, CS) theory is exactly to be arisen at the historic moment according to such hypothesis.Compressive sensing theory points out, if
Signal is compressible or is sparse in some transform domain, then can be incited somebody to action by one with the incoherent observing matrix of transform domain
High dimensional signal is projected in lower dimensional space, then high by the reconstruct of solving-optimizing problem high probability from a small amount of low-dimensional data
Dimensional signal.And this utilization compressed sensing principle converts analog signals into data signal, and therefrom extract the device of sparse information
Part is referred to as analog information converter (Analog-to-Information Convertor, AIC).Analog information converter one
As include frequency mixer, simulation low-pass filter and sampling unit, wherein, frequency mixer is used for initial signal and pseudo-random sequence
(Pseudo-Noise sequence) signal is mixed, and the low frequency part in mixed signal, which is contained, can express original
The important information of signal;Simulation low-pass filter is used to be filtered the signal after mixing, by the low of the mixed signal
Frequency extracting section comes out;Sampler is used to sample to filtered signal, and the sampling unit is generally ADC.
In order to realize the compressed sensing to signal, it is necessary to meet the incoherent condition of any two row of the observing matrix,
The design of the condition and simulation low-pass filter is closely bound up, and the design of simulation low-pass filter is unreasonable, be able to not will meet
The condition, perception is compressed to signal so as to can not realize.In summary, prior art needs one kind to realize compression sense
The simulation low-pass filter known.
The content of the invention
In order to solve the above-mentioned technical problem, AIC analog low-pass filter can be applied to the embodiments of the invention provide a kind of
Ripple device, a kind of it can realize the analog information converter and a kind of filtering method of compressed sensing.
In a first aspect, the embodiments of the invention provide a kind of simulation low-pass filter, the simulation low-pass filter includes:
Adder unit, state conversion unit, first delay cell and at least one second delay cell;
Wherein, the output end of the state conversion unit is connected with the adder unit, the state conversion unit it is defeated
Enter end to be connected with first delay cell, the adder unit and first delay cell connection;
The output end and input of the state conversion unit are connected with least one described second delay cell respectively;
The adder unit, for the mixed frequency signal for receiving the simulation low-pass filter and from the State Transferring
The signal of unit, which is overlapped, obtains composite signal, and the composite signal is input into first delay cell, described mixed
Frequency signal is the signal after initial signal is mixed with random sequence signal;
First delay cell, the delay for carrying out the unit interval to the composite signal from the adder unit,
And the signal after first delay units delay is input to the state conversion unit;
At least one described second delay cell, for carrying out the unit interval to the signal from the state conversion unit
Delay, and the signal after the delay by least one second delay cell is input to the state conversion unit;
The state conversion unit, for using loop cycle matrix to from first delay cell and it is described at least
The signal of one the second delay cell is weighted processing, and the signal after weighting corresponded to respectively input to the adder and
At least one described second delay cell;The parameter of the loop cycle matrix is rushed according to the frequency domain of the simulation low-pass filter
The coefficient for swashing receptance function is obtained, and the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse
Any two row for the calculation matrix that receptance function and sampling function are obtained are uncorrelated;
One of them second delay cell in first delay cell, or at least one described second delay cell,
It is additionally operable to being input to the signal after delay into the sampler being connected with the simulation low-pass filter.
In the first possible implementation of first aspect, in the frequency domain impulse response function H at j momentj(z) it is:
Wherein, i numbers for the moment, and T is the cycle of the loop cycle matrix, row vector or column vector that N is A (t)
Number, λ 'k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,j
For Ψ (i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
With reference to the first possible implementation of first aspect, in second of possible implementation, the measurement
Any two row of matrix are uncorrelated specifically to be represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;
ΦiFor D (z) Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to that Fourier becomes
Change;FΦj=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding measurements of moment j
Matrix, F refers to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F
Φj||2To seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
With reference to the first possible implementation of first aspect, in the third possible implementation, the condition
Also include:The limit of system is in unit circle.
With reference to the third possible implementation of first aspect, in the 4th kind of possible implementation, the system
Limit represented in unit circle with equation below:
Wherein, | | λ 'k,i,j||2To seek λ 'k,i,jMould 2 norms.
With reference to the first possible implementation of first aspect, in the 4th kind of possible implementation, the condition
Also include:System pole is more than or equal to preset value.
With reference to the 4th kind of possible implementation of first aspect, in the 5th kind of mode in the cards, the system
Limit is represented more than or equal to preset value by equation below:
min{||λ'k,i,j||2}≥γ
Wherein, the γ is preset value, represents lower bound of the limit apart from origin.
With reference in a first aspect, in the 6th kind of mode in the cards, the condition also includes:The loop cycle matrix
Parameter within a preset range.
Second aspect, the embodiments of the invention provide a kind of analog information converter, the analog information converter includes
Any possible implementation in first to the 6th kind of frequency mixer, sampler and first aspect and first aspect
Simulation low-pass filter, the frequency mixer is connected with the simulation low-pass filter, and the simulation low-pass filter is adopted with described
Sample device is connected;
The frequency mixer, for initial signal to be mixed with random sequence signal, obtains mixed frequency signal;
The simulation low-pass filter, for being filtered to the mixed frequency signal, obtains filtering signal;
The sampler, for being sampled to the filtering signal.
The third aspect, the embodiments of the invention provide a kind of analog information converter, including:
Processor;
Memory;And COM1;
Wherein, the processor is used for the instruction for performing the memory storage, to perform following step in execute instruction
Suddenly:
Received by the COM1 come the mixed frequency signal of self-mixing device, the mixed frequency signal is initial signal and random
Signal after sequence signal mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped with the signal after weighting and obtains composite signal;
The delay of unit interval is carried out to the composite signal, and prolonging for unit interval is carried out to the signal after the weighting
Late;
The signal after processing obtains the weighting is weighted to the signal by delay using loop cycle matrix;
The parameter of the loop cycle matrix is obtained according to the coefficient of the frequency domain impulse response function of the simulation low-pass filter, described
The coefficient of frequency domain impulse response function meets following condition:The survey obtained according to the frequency domain impulse response function and sampling function
Any two row of moment matrix are uncorrelated;
Signal after delay is input to by the sampler being connected with the simulation low-pass filter by the COM1.
In the first possible implementation of the third aspect, in the frequency domain impulse response function H at j momentj(z) it is:
Wherein, i numbers for the moment, and T is the cycle of the loop cycle matrix, row vector or column vector that N is A (t)
Number, λ 'k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,j
For Ψ (i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
With reference to the first possible implementation of the third aspect, in second of possible implementation, the measurement
Any two row of matrix are uncorrelated specifically to be represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;
ΦiFor D (z) Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to that Fourier becomes
Change;FΦj=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding measurements of moment j
Matrix, F refers to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F
Φj||2To seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
In the third possible implementation of the third aspect, the condition also includes:The limit of system is in unit circle
It is interior.
In the 4th kind of possible implementation of the third aspect, the condition also includes:System pole is more than or equal to
Preset value.
In the 5th kind of possible implementation of the third aspect, the condition also includes:The loop cycle matrix
Parameter is within a preset range.Fourth aspect, the embodiments of the invention provide a kind of filtering method, methods described includes:
Simulation low-pass filter receives the mixed frequency signal for carrying out self-mixing device, and the mixed frequency signal is initial signal and stochastic ordering
Signal after column signal mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped and obtains composite signal by the simulation low-pass filter with the signal after weighting;
The simulation low-pass filter carries out the delay of unit interval to the composite signal, and to the letter after the weighting
Number carry out the unit interval delay;
The simulation low-pass filter is weighted to the signal by delay using loop cycle matrix and handled
Signal to after the weighting;The parameter of the loop cycle matrix is according to the frequency domain impulse response of the simulation low-pass filter
The coefficient of function is obtained, and the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response letter
Any two row for the calculation matrix that number and sampling function are obtained are uncorrelated;
Signal after delay is input to the sampling being connected with the simulation low-pass filter by the simulation low-pass filter
Device.
In the first possible implementation of fourth aspect, in the frequency domain impulse response function H at j momentj(z) it is:
Wherein, i numbers for the moment, and T is the cycle of the loop cycle matrix, row vector or column vector that N is A (t)
Number, λ 'k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,j
For Ψ (i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
With reference to the first possible implementation of fourth aspect, in second of possible implementation, the measurement
Any two row of matrix are uncorrelated specifically to be represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;
ΦiFor D (z) Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to that Fourier becomes
Change;FΦj=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding measurements of moment j
Matrix, F refers to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F
Φj||2To seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
In the third possible implementation of fourth aspect, the condition also includes:The limit of system is in unit circle
It is interior.
In the 4th kind of possible implementation of fourth aspect, the condition also includes:System pole is more than or equal to
Preset value.
In the 5th kind of possible implementation of fourth aspect, the condition also includes:The loop cycle matrix
Parameter is within a preset range.
5th aspect, the embodiments of the invention provide a kind of filtering method, methods described is applied to first aspect and first
The first of aspect is into the possible implementation of any of which in the 6th kind, and the filtering method includes:
The mixed frequency signal for carrying out self-mixing device is received, the mixed frequency signal is after initial signal is mixed with random sequence signal
Signal, the frequency mixer is connected with the simulation low-pass filter;
The mixed frequency signal is overlapped and closed by the adder unit with the signal from the state conversion unit
Into signal;
First delay cell carries out the delay of unit interval to the composite signal from the adder unit;
At least one described second delay cell carries out prolonging for unit interval to the signal from the state conversion unit
Late;
The state conversion unit using loop cycle matrix to from first delay cell and it is described at least one
The signal of second delay cell is weighted processing, and the signal after weighting is corresponded to input respectively to the adder and described
At least one second delay cell;The parameter of the loop cycle matrix is rung according to the frequency domain impulse of the simulation low-pass filter
The coefficient of function is answered to obtain, the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response
Any two row for the calculation matrix that function and sampling function are obtained are uncorrelated;
It is single using one of them second delay in first delay cell, or at least one described second delay cell
Member, the signal after delay is input to the sampler being connected with the simulation low-pass filter.
In the first possible implementation of the 5th aspect, in the frequency domain impulse response function H at j momentj(z) it is:
Wherein, i numbers for the moment, and T is the cycle of the loop cycle matrix, row vector or column vector that N is A (t)
Number, λ 'k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,j
For Ψ (i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
With reference to the first possible implementation of the 5th aspect, in second of possible implementation, the measurement
Any two row of matrix are uncorrelated specifically to be represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;
ΦiFor D (z) Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to that Fourier becomes
Change;FΦj=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding measurements of moment j
Matrix, F refers to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F
Φj||2To seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
In the third possible implementation of the 5th aspect, the condition also includes:The limit of system is in unit circle
It is interior.
In the 4th kind of possible implementation of the 5th aspect, the condition also includes:System pole is more than or equal to
Preset value.
In the 5th kind of possible implementation of the 5th aspect, the condition also includes:The loop cycle matrix
Parameter is within a preset range.
Mixed frequency signal is inputted addition list by the simulation low-pass filter that the present invention is designed it can be seen from above-mentioned technical proposal
After member, by adder unit being superimposed mixed frequency signal and the signal from state conversion unit and by by the first delay
The circular treatment that unit, at least one second delay cell and state conversion unit are postponed, weighted, is realized to mixing letter
Number filtering.
Wherein, the analogue low pass filtering that the parameter of loop cycle matrix is designed according to the present invention in the state conversion unit
The frequency domain impulse response function that device is obtained is obtained, and the parameter for the frequency domain impulse response function that the simulation low-pass filter is obtained is needed
The incoherent condition of any two row of calculation matrix is met, so that simulation low-pass filter can be applied to analog information conversion
Device, the frequency domain impulse response function and sampling function that the calculation matrix is obtained according to the simulation low-pass filter is obtained.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, without having to pay creative labor, may be used also
To obtain other accompanying drawings according to these accompanying drawings.
Fig. 1 is a kind of structural representation for simulation low-pass filter that the embodiment of the present invention one is provided;
Fig. 2 is the structural representation for the second order simulation low-pass filter that the embodiment of the present invention one is provided;
Fig. 3 is a kind of structural representation for analog information converter that the embodiment of the present invention two is provided;
Fig. 4 is a kind of structural representation for analog information converter that the embodiment of the present invention three is provided.
Embodiment
Before technical scheme is introduced, the basic theories of compressed sensing is introduced first.It is assumed that signal can
Represented using the signal x (signal vector) using a length as n, when signal x is with one group of orthogonal basisWhen linear combination is represented,
I.e.Wherein Ψ is sparse transformation basic matrix.If projection coefficient θ only has K significant coefficient (i.e. definitely
Value very big coefficient relatively), and K is much smaller than n, it is openness that we just say that signal x has, and signal x is also referred to as K- sparse signals.
Because signal x is sparse, therefore it can be compressed, it is assumed that the signal obtained after overcompression is y (signal vector), length is
M, and m is much smaller than n, then signal y can be referred to as observation vector.Observation vector is the linear projection of signal vector, this throwing
Shadow process can represent with calculation matrix Φ, i.e. y=Φ x, wherein, calculation matrix Φ is a rank deficient matrix.That is, false
If projection coefficient is (θ1,θ2,…,θn), sparse transformation basic matrix Ψ isCalculation matrix Φ isSo
Because m is much smaller than n, it is achieved that the purpose of compressed signal.In addition, Φ and Ψ product A is called observing matrix by we.
Signal y after compression has been obtained is, it is necessary to which restoring it can just use for signal x.In order to realize that signal recovers,
It has to be ensured that the correlation of observing matrix A (A=Φ Ψ) any two row is as small as possible.Because sparse transformation basic matrix Ψ is
It is relatively-stationary, therefore it is as small as possible to only need to ensure the correlation of calculation matrix Φ any two row.
In the embodiment of the present invention, the compressed sensing to primary signal is realized using analog information converter AIC, i.e., according to such as
Upper described principle carries out sampling in compression to signal.Based on above-mentioned analysis, in order to realize the requirement of compressed sensing, AIC
Design need to ensure that the correlations of calculation matrix Φ any two row are as small as possible.And for AIC, it generally comprises three
Individual part, is frequency mixer, low-pass analog filter and sampler respectively, in this three, can be based on low-passed analog filter
The low-passed analog filter function of ripple device and the sampling function of the sampler obtain the calculation matrix Φ.Due to sampling function one
As it is only related to sample rate, become more readily available, therefore, in AIC design, the design of simulation low-pass filter is just particularly closed
Key.It should be reached by the design to simulation low-pass filter so that uncorrelated this requirement of any two row of the calculation matrix Φ,
So as to the need for meeting compressed sensing.
In the present invention, inventor designs a simulation low-pass filter first, according to each list in the simulation low-pass filter
The annexation of member, determines the relational expression of the frequency domain impulse response function of the simulation low-pass filter, based on the measurement square
Correlation this requirement as small as possible of any two row of battle array Φ, it is determined that the value of a variable in the relational expression is obtained, with reference to this
The value of variable, it is determined that the matrix parameter of corresponding units in the simulation low-pass filter is drawn, so as to complete for institute in AIC
State the design of simulation low-pass filter.Above-mentioned design is described in detail below.
First, the design of the composition of simulation low-pass filter and annexation
In the present invention, the simulation low-pass filter includes adder unit, state conversion unit, a first delay list
At least one first second delay cell.The output end of the state conversion unit is connected with the adder unit, and the state turns
The input for changing unit is connected with the first delay cell end, the adder unit and first delay cell connection;Institute
The output end and input for stating state conversion unit are connected with least one described second delay cell respectively.The addition list
Member, is overlapped with the signal from state conversion unit for the mixed frequency signal for receiving the simulation low-pass filter, obtains
First delay cell is input to composite signal, and by the composite signal.First delay cell, for from
The composite signal of the adder unit carries out the delay of unit interval, and the signal Jing Guo first delay units delay is defeated
Enter to the state conversion unit.At least one described second delay cell, for the letter from the state conversion unit
The delay of unit interval number is carried out, and the signal after the delay by least one second delay cell is input to described
State conversion unit.The state conversion unit, for utilizing loop cycle matrix to from first delay cell and institute
The signal for stating at least one the second delay cell is weighted processing, and the signal after weighting corresponded to respectively input to it is described extremely
Few second delay cell and the adder, to be circulated.First delay cell, or it is described at least one second
One of them second delay cell in delay cell, is additionally operable to the signal after delay being input to and the analogue low pass filtering
The sampler of device connection.
According to the above-mentioned composition and annexation of simulation low-pass filter, frequency domain impulse response function H can be obtainedj(z)。
2nd, the parameter of the loop cycle matrix in state conversion unit determines whether simulation low-pass filter can be applied
Key in AIC systems is the determination of loop cycle matrix parameter, the most important condition that the loop cycle matrix parameter is met
It is exactly that any two row of calculation matrix are uncorrelated.Because filter function Hj(z) parameter is determined by the parameter of loop cycle matrix
Fixed, and the calculation matrix is by frequency domain impulse response function Hj(z) determined with sampling function D (z) product, described
Sampling function D (z) is known, frequency domain impulse response function Hj(z), it is known that but frequency domain impulse response function Hj(z) feelings of unknown parameters
Under condition, according to frequency domain impulse response function Hj(z) matrix carried out again after Fourier transformation that is multiplied with sampling function D (z) is any
Two row are uncorrelated, can obtain frequency domain impulse response function Hj(z) coefficient, then according to the frequency domain impulse response function Hj
(z) the anti-parameter for releasing loop cycle matrix of coefficient.
Embodiment one:
The operation principle of simulation low-pass filter based on above-mentioned introduction, the present invention provides a kind of simulation applied to AIC
The embodiment of low pass filter, referring to Fig. 1, the simulation low-pass filter includes:
Adder unit 101, state conversion unit 102, first delay cell 103 and at least one second delay cell
104。
Wherein, the output end of the state conversion unit 102 is connected with the adder unit 101, the State Transferring list
The input of member 102 is connected with first delay cell 103, and the adder unit 101 and first delay cell 103 connect
Connect;
The output end and input of the state conversion unit 102 respectively with least one described second delay cell 104
Connection.
The adder unit 101, for the mixed frequency signal for receiving the simulation low-pass filter and from State Transferring
The signal of unit 102 is overlapped, and obtains composite signal.The mixed frequency signal comes from frequency mixer, specifically, the frequency mixer
Initial signal is mixed with random sequence signal, the mixed frequency signal is obtained.
First delay cell 103, for carrying out the unit interval to the composite signal from the adder unit 101
Delay, and the signal after first delay cell 103 postpones is input to the state conversion unit 102.
At least one described second delay cell 104, it is single for being carried out to the signal from the state conversion unit 102
The delay of position time, and the signal after the delay by least one second delay cell 104 is input to the state
Converting unit 102;
The state conversion unit 102, for utilizing loop cycle matrix to from first delay cell 103 and institute
The signal for stating at least one the second delay cell 104 is weighted processing, and the signal after weighting is corresponded into input respectively to institute
Adder 101 and at least one described second delay cell 103 are stated, to be circulated.The loop cycle matrix refers to parameter
The characteristics of periodically variable circular matrix, circular matrix is that each parameter of row vector is each of previous row row vector
Individual parameter moves right the result of a position successively.In the present embodiment, the loop cycle matrix can be expressed as:
The loop cycle matrix has the characteristic of mechanical periodicity, that is, A (t)=A (t+T), T are the loop cycle
The cycle of matrix.When the T is 0, constant matrix when the loop cycle matrix is referred to as, it is adaptable to steady random initial letter
Number, the steady random any n dimension distribution functions for being meant that signal or probability density function are unrelated with start time;Work as institute
State T more than 0 when, the loop cycle matrix be time-varying matrix, it is adaptable to the random initial signal of non-stationary, the non-stationary with
Machine refers to that any n dimension distribution functions or probability density function of signal are related to start time.
The parameter of the loop cycle matrix is according to the coefficient of the frequency domain impulse response function of the simulation low-pass filter
Obtain, the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response function and sampling letter
Any two row for the calculation matrix that number is obtained are uncorrelated.
First delay cell 103, is additionally operable to the signal after first delay cell 103 is postponed and is input to and institute
State the sampler of simulation low-pass filter connection;Or, at least one described second delay cell 104 one of them second
Delay cell 104, is additionally operable to the signal after second delay cell 104 is postponed and is input to and simulation low-pass filter company
The sampler connect.
Below the analog low-pass filter is introduced by taking first delay cell 103 and one second delay unit 104 as an example
The operation principle of ripple device.Referring to Fig. 2, it is assumed that the mixed frequency signal of t down-conversion mixers output is not x (t), the loop cycle in the same time
MatrixMixed frequency signal x (t) input is to adder unit 101, by described 101 pairs of institutes of adder unit
State mixed frequency signal x (t) and the signal y from state conversion unit 1021(t) synthesized, the signal after synthesis is z (t).Close
Into delays of the signal z (t) Jing Guo the first delay cell 103, as signal x1(t), the signal x1(t) it is divided into two-way, it is defeated all the way
Go out, another road is inputted to state conversion unit 102.Meanwhile, the signal x from the second delay cell 1042(t) shape is also input to
State converting unit 102.The signal x1(t) with signal x2(t) signal vector, the cycle with the state conversion unit 102 are constituted
Circular matrix A (t) is multiplied, with to signal x1(t) with signal x2(t) it is weighted, and exports the signal y after weighting1And y (t)2
(t), wherein signal y1(t) input to adder unit 101, signal y2(t) input is to the second delay cell 104, to carry out next time
Circulation.
Specifically, assume that x (0), x (1), x (2) they are respectively the mixed frequency signal of frequency mixer output at moment t=0,1,2,
Wherein t=0 represents initial time.Assuming that A (0), A (1), A (2) are respectively the corresponding loop cycle square at moment t=0,1,2
Battle array, wherein, z(0)、z(1)、
Z (2) is respectively the signal that adder unit 101 is exported at moment t=0,1,2;x1(0)、x1(1)、x1(2) it is respectively in moment t
The signal that first delay cell 103 is exported when=0,1,2;x2(0)、x2(1)、x2(2) it is respectively at moment t=0,1,2 second
The signal that delay cell 103 is exported;y1(0)、y1(1)、y1(2) be respectively at moment t=0,1,2 state conversion unit 102 to
The signal that adder unit 101 is exported;y2(0)、y2(1)、y2(2) be respectively at moment t=0,1,2 state conversion unit 102 to
The signal of second delay cell 104 output.
As t=0, it can obtain:
Z (0)=x (0)
x1(0)=0, x2(0)=0
y1(0)=0, y2(0)=0
It should be noted that at the t=0 moment, mixed frequency signal x (0) passes through adder unit 101, due to it is initial when y1(0)=
0, therefore the composite signal z (0) of output adder unit 101 remains as mixed frequency signal x (0).
As t=1, it can obtain:
x1(1)=z (0)=x (0), x2(1)=0
Z (1)=y1(1)+x(1)
It should be noted that at the t=1 moment, signal x (0) have passed through the first delay cell 103 and be changed into x1(1), but letter
Number x1(1) it is identical with signal x (0) value.And the time that first delay cell 103 postpones, i.e. unit interval, it is exactly t=1
With t=0 time difference.Moreover, at the t=1 moment, second delay cell 104 does not have signal outflow, therefore signal x2(1)
Value be 0.
As t=2, it can obtain:
x1(2)=z (1)=y1(1)+x (1)=a1(1)x(0)+x(1)
x2(2)=y2(1)=a2(1)x(0)
Z (2)=y1(2)+x (2)=(a1(2)a1(1)+a2(2)a2(1))x(0)+a1(2)x(1)+x(2)
The structure and operation principle of simulation low-pass filter are mainly described above, in order to apply in AIC systems
In, realize the compression to signal, in addition it is also necessary to which the parameter in loop cycle matrix is designed.The cycle is described in detail below
The calculating process of the parameter of circular matrix.
First, the low-pass analog filter designed according to the present embodiment, can obtain moment j frequency domain impulse response function
Hj(z):
Wherein, i be the moment numbering, T be loop cycle matrix cycle, N for A (t) row vector or column vector number,
λ'k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,jFor Ψ
(i-1, k-th of characteristic value j).
Function Ψ (n2,n1) definition be:
Wherein I is that the element on unit matrix, i.e. the matrix upper left corner to the diagonal (being referred to as leading diagonal) in the lower right corner is equal
For 1, other elements are all 0.
Therefore it can obtain:
Wherein A (t) is loop cycle matrix.
The physical meaning of so-called characteristic value is:Assuming that matrix A (such as Ψ (T, 0), Ψ (i-1,0) Ψ (T, j), Ψ (i-1,
J)) it can be expressed as:Ax=ax, wherein a are not 0, then a is representing matrix A characteristic value, and corresponding characteristic vector is x.Can
To think that matrix A has embodiment on characteristic vector x direction, and it is a in characteristic vector x embodiment value.If a is bigger, square is represented
The power contributed in the x direction of battle array A is bigger, and information content is more, and be here used for solving the simulation low-pass filter is
Number.
Obtaining moment j frequency domain impulse response function Hj(z) after, it is assumed that the corresponding sampling function of sampler 31 is D
(z), by the frequency domain impulse response function Hj(z) obtained after being multiplied with sampling function D (z):
FΦj=D (z) Hj(z) (2)
Wherein, ΦjFor D (z) Hj(z) function after Fourier transformation, that is, calculation matrix.F refers to that Fourier becomes
Change.
As previously described, in order to realize that simulation low-pass filter can be applied to AIC systems, the compression sense of signal is realized
Know, it is necessary to ensure that the correlation of any two row of calculation matrix is uncorrelated, but in actual applications for various reasons, this
Part can not almost be realized, therefore ensure that the correlation of any two row of calculation matrix is as small as possible, thus have following condition:
Wherein, F ΦiFor the corresponding calculation matrix of moment i, F ΦjFor the corresponding calculation matrix of moment j, (F Φi)HFor to F
ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F Φj||2To seek F ΦjMould 2 norms, the δ is
Waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.That is, calculation matrix F ΦjThe correlation of any two row
Property be less than or equal to default waviness tolerance value δ, you can think calculation matrix F ΦjAny two row are uncorrelated.
In summary, because inventor devises the low-pass analog filter of said structure, therefore frequency domain punching can be obtained
Swash receptance function Hj(z), the frequency domain impulse response function Hj(z) parameter is the ginseng according to the loop cycle matrix A (t)
What number was obtained.According to the frequency domain impulse response function Hj(z) product with sampling function D (z) can obtain calculation matrix, profit
The condition of uncorrelated (i.e. formula (3)) is arranged with the calculation matrix any two, frequency domain impulse response function H can be obtainedj(z)
Parameter, then can utilize frequency domain impulse response function Hj(z) parameter instead releases loop cycle matrix A (t) according to formula (1)
Parameter.After the parameter for obtaining loop cycle matrix A (t), it is possible to by the low-pass analog filter realization pair of said structure
The compressed sensing of signal.
In addition, in actual applications, the frequency domain impulse response function H of the low-pass analog filterj(z) parameter except
The incoherent condition of any two row of calculation matrix is met, following condition should be also met:
1st, as simulation low-pass filter, in addition it is also necessary to which guarantee system is stable in itself, so-called system is stable to be sought to protect
All limits of card system are all in unit circle, and the limit represents the position of simulation low-pass filter passband, the unit circle
It is 0 to refer to origin, the circle for the point composition for being 1 apart from the Euclidean distance of origin.Need to meet following condition:
Wherein, | | λ 'k,i,j||2To seek λ 'k,i,jMould 2 norms, λ 'k,i,jImplication referring to formula (1).
In the present embodiment, when loop cycle matrix meets the condition of formula (3) and formula (4), it is possible to ensureing mould
Intend low pass filter on the basis of its own system is stable, the simulation low-pass filter for designing the present embodiment is applied to AIC, real
The compressed sensing of existing signal.
2nd, the information of more input values is carried, it is necessary to allow in observation in order to ensure higher recovery probability, therefore
Need to ensure that there is simulation low-pass filter longer system to respond during design.In order to reach this purpose, the condition is also wrapped
Include:System pole is more than or equal to preset value, is specifically represented with formula (5).
min{||λ'k,i,j||2}≥γ (5)
Wherein, the γ is preset value, represents lower bound of the limit apart from origin.
3rd, in order to ensure convergence of algorithm speed, in the parameter of calculating cycle circular matrix, it can be made in default model
Interior value is enclosed, for example [- 5,5].
Embodiment two:
The simulation low-pass filter designed based on inventor, the present invention also provides a kind of analog information converter, joins
See Fig. 3, the analog information converter includes frequency mixer 11, simulation low-pass filter 21 and sampler 31.The frequency mixer 11
Connected with the simulation low-pass filter 21, the simulation low-pass filter 21 and the sampler 31 are attached.
Initial signal is mixed by the frequency mixer 11 with random sequence signal, obtains mixed frequency signal.
The frequency mixer 11 can not do specific limit using all frequency mixers suitable for AIC in the prior art, the present invention
It is fixed.Frequency mixer 11 is used to initial signal being mixed with random sequence signal, wherein, the random sequence signal is general by one
Individual takes the random sequence of { ± 1 } two kinds of values to constitute, and in order to be mixed all initial signals obtained in bandwidth, the stochastic ordering
The sample rate of column signal is higher than the sample rate of initial signal.The part letter of the feature of initial signal can be expressed in mixed frequency signal
The low frequency part of mixed frequency signal number is just concentrated on, so passes through simulation low-pass filter 21, it is possible to by the low frequency of mixed frequency signal
Extracting section comes out, and realizes the compression to initial signal.
The composition and annexation of the simulation low-pass filter 21 are referring to embodiment one, and the present embodiment is repeated no more.
The sampler 31, for being sampled to the filtering signal.
Due to the filtering signal exported from simulation low-pass filter 21, its highest frequency is less than the most high frequency of initial signal
Rate, according to Nyquist's theorem, the sampling rate of the sampler 31 will be less than the sampling directly sampled to initial signal
Speed, that is, reduce the requirement to the sampling rate of sampler 31.
In actual applications, the sampler 31 can use all samplers suitable for AIC systems, and the present invention is not done
It is specific to limit.In the present embodiment, the sampler 31 is ADC (Analog to Digital Converter, analog-to-digital conversion
Device).
Embodiment three
In order to further reduce the requirement to sampler samples rate, the AIC systems of inventor's design are included parallel at least
Frequency mixer, simulation low-pass filter and the sampler mentioned in two sets of embodiments one, the mould provided referring to Fig. 4, the present embodiment
Intending transcriber includes at least one frequency mixer 51, at least one simulation low-pass filter 52 and at least one sampler 53,
Wherein, the quantity of these three devices is identical, and the function of this three classes device is low with the frequency mixer 11 in embodiment one, simulation respectively
Bandpass filter 21 and sampler 31 are identical, and here is omitted.It should be noted that in order to ensure AIC systematic survey matrixes
The correlation of any two row is as small as possible, and the random sequence signal in each frequency mixer 51 should be different, and each mould
Corresponding loop cycle matrix is different in plan low pass filter 52, and the parameter of each loop cycle matrix needs each mould of simultaneous
Intend the condition that should meet of low pass filter 52 to solve.
Because the random sequence signal in frequency mixer 51 is different, and corresponding week in each simulation low-pass filter 52
Phase circular matrix is also different, thus while input to AIC signal is identical, but from each simulation low-pass filter
The signal of 52 outputs is different, is sampled respectively by each signal to output, it is possible to obtain different sampled datas, real
Requirement of the reduction to the sample rate of sampler 53 is showed.For example, it is assumed that the sample rate for requiring sampler 53 is fs, if there is two groups to mix
Frequency device, simulation low-pass filter and sampler, then the sample rate of each sampler can be just fs/2.Group number is more, to every
The requirement of the sample rate of individual sampler is lower.
It should be noted that each unit in the simulation low-pass filter mentioned in the embodiment one to three can be used
Software is realized, can also be realized by hardware, for example adder unit can be realized by adder, and delay cell, which can be utilized, prolongs
Slow device realizes that state conversion unit can be realized using memory and adder, specifically, adder, delayer, can pass through
Resistance, operational amplifier, electric capacity, diode etc. are realized.In this regard, the present invention is not specifically limited, those skilled in the art can
Voluntarily to select according to the actual requirements.If realized using software, if for example using matlab instruments, (matlab is individual soft
Part), frequency mixer, adder, the delayer model buildings in matlab simulink instruments can be used, respective devices are realized
Function;If using matlab code, frequency mixer is just directly with " * " order, z=x*y, adder "+" order, i.e. z
=x+y, delayer is with z (n)=x (n-1), to simulate the function of respective devices.
Example IV
The simulation low-pass filter provided based on embodiment one, the present invention also provides a kind of embodiment of filtering method, institute
State in the simulation low-pass filter that filtering method is referred to applied to embodiment one to three, methods described includes:
The mixed frequency signal for carrying out self-mixing device is received, the mixed frequency signal is after initial signal is mixed with random sequence signal
Signal, the frequency mixer is connected with the simulation low-pass filter;
The mixed frequency signal is overlapped and closed by the adder unit with the signal from the state conversion unit
Into signal;
First delay cell carries out the delay of unit interval to the composite signal from the adder unit;
At least one described second delay cell carries out prolonging for unit interval to the signal from the state conversion unit
Late;
The state conversion unit using loop cycle matrix to from first delay cell and it is described at least one
The signal of second delay cell is weighted processing, and the signal after weighting is corresponded to input respectively to the adder and described
At least one second delay cell;The parameter of the loop cycle matrix is rung according to the frequency domain impulse of the simulation low-pass filter
The coefficient of function is answered to obtain, the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response
Any two row for the calculation matrix that function and sampling function are obtained are uncorrelated;
It is single using one of them second delay in first delay cell, or at least one described second delay cell
Member, the signal after delay is input to the sampler being connected with the simulation low-pass filter.
The operation principle of the filtering method provided on the present embodiment specifically refers to embodiment one, and here is omitted.
Embodiment five
The simulation low-pass filter provided based on embodiment one, the present invention also provides a kind of another implementation of filtering method
Example, methods described includes:
Simulation low-pass filter receives the mixed frequency signal for carrying out self-mixing device, and the mixed frequency signal is initial signal and stochastic ordering
Signal after column signal mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped and obtains composite signal by the simulation low-pass filter with the signal after weighting;
The simulation low-pass filter carries out the delay of unit interval to the composite signal, and to the letter after the weighting
Number carry out the unit interval delay;
The simulation low-pass filter is weighted to the signal by delay using loop cycle matrix and handled
Signal to after the weighting;The parameter of the loop cycle matrix is according to the frequency domain impulse response of the simulation low-pass filter
The coefficient of function is obtained, and the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response letter
Any two row for the calculation matrix that number and sampling function are obtained are uncorrelated;
Signal after delay is input to the sampling being connected with the simulation low-pass filter by the simulation low-pass filter
Device.
The operation principle of the filtering method provided on the present embodiment specifically refers to embodiment one, and here is omitted.
Embodiment six
The present invention also provides the embodiment of another simulation low-pass filter, and the simulation low-pass filter includes:
Processor;
Memory;And COM1;
Wherein, the processor is used for the instruction for performing the memory storage, to perform following step in execute instruction
Suddenly:
Received by the COM1 come the mixed frequency signal of self-mixing device, the mixed frequency signal is initial signal and random
Signal after sequence signal mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped with the signal after weighting and obtains composite signal;
The delay of unit interval is carried out to the composite signal, and prolonging for unit interval is carried out to the signal after the weighting
Late;
The signal after processing obtains the weighting is weighted to the signal by delay using loop cycle matrix;
The parameter of the loop cycle matrix is obtained according to the coefficient of the frequency domain impulse response function of the simulation low-pass filter, described
The coefficient of frequency domain impulse response function meets following condition:The survey obtained according to the frequency domain impulse response function and sampling function
Any two row of moment matrix are uncorrelated;
Signal after delay is input to by the sampler being connected with the simulation low-pass filter by the COM1.
The operation principle of the simulation low-pass filter provided on the present embodiment specifically refers to embodiment one, herein no longer
Repeat.
" first " for the first router mentioned in the embodiment of the present invention is used only to do name mark, not representative order
On first.The rule is equally applicable to " second ".
It should be noted that each embodiment in this specification is described by the way of progressive, each embodiment it
Between identical similar part mutually referring to what each embodiment was stressed is the difference with other embodiment.
For embodiment two to six, because it is substantially similar to embodiment one, so describe fairly simple, correlation
Place illustrates referring to the part of embodiment one.Device embodiment described above is only schematical, is divided wherein being used as
Unit from part description can be or may not be it is physically separate, the part shown as unit can be or
It may not be physical location, you can with positioned at a place, or can also be distributed on multiple NEs.Can basis
Some or all of module therein is selected to realize the purpose of this embodiment scheme the need for reality.Ordinary skill people
Member is without creative efforts, you can to understand and implement.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in,
It should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims
It is defined.
Claims (21)
1. a kind of simulation low-pass filter, it is characterised in that the simulation low-pass filter includes:
Adder unit, state conversion unit, first delay cell and at least one second delay cell;
Wherein, the output end of the state conversion unit is connected with the adder unit, the input of the state conversion unit
It is connected with first delay cell, the adder unit and first delay cell connection;
The output end and input of the state conversion unit are connected with least one described second delay cell respectively;
The adder unit, for the mixed frequency signal for receiving the simulation low-pass filter and from the state conversion unit
Signal be overlapped and obtain composite signal, and the composite signal is input to first delay cell, the mixing letter
Signal after number being mixed for initial signal and random sequence signal;
First delay cell, the delay for carrying out the unit interval to the composite signal from the adder unit, and will
Signal after first delay units delay is input to the state conversion unit;
At least one described second delay cell, for carrying out prolonging for unit interval to the signal from the state conversion unit
Late, and by the signal after the delay by least one second delay cell it is input to the state conversion unit;
The state conversion unit, for using loop cycle matrix to from first delay cell and it is described at least one
The signal of second delay cell is weighted processing, and the signal after weighting is corresponded to input respectively to the adder and described
At least one second delay cell;The parameter of the loop cycle matrix is rung according to the frequency domain impulse of the simulation low-pass filter
The coefficient of function is answered to obtain, the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response
Any two row for the calculation matrix that function and sampling function are obtained are uncorrelated;
One of them second delay cell in first delay cell, or at least one described second delay cell, is also used
Signal after by delay is input to the sampler being connected with the simulation low-pass filter.
2. simulation low-pass filter according to claim 1, it is characterised in that in the frequency domain impulse response function H at j momentj
(z) it is:
Wherein, i be the moment numbering, T be the loop cycle matrix cycle, N for A (t) row vector or column vector number,
λ′k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,jFor Ψ
(i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
3. simulation low-pass filter according to claim 2, it is characterised in that any two row of calculation matrix are uncorrelated
Specifically represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;ΦiFor D
(z)Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to Fourier transformation;FΦj
=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment j, F is
Refer to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F Φj||2For
Seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
4. simulation low-pass filter according to claim 2, it is characterised in that the condition also includes:The limit of system
In unit circle.
5. simulation low-pass filter according to claim 4, it is characterised in that the limit of the system is used in unit circle
Equation below is represented:
Wherein, | | λ 'k,i,j||2To seek λ 'k,i,jMould 2 norms.
6. simulation low-pass filter according to claim 2, it is characterised in that the condition also includes:System pole is big
In or equal to preset value.
7. simulation low-pass filter according to claim 6, it is characterised in that the system pole is more than or equal to default
Value is represented by equation below:
min{||λ′k,i,j||2}≥γ
Wherein, the γ is preset value, represents lower bound of the limit apart from origin.
8. simulation low-pass filter according to claim 1, it is characterised in that the condition also includes:The cycle is followed
The parameter of ring matrix is within a preset range.
9. a kind of analog information converter, it is characterised in that the analog information converter include frequency mixer, sampler and
The simulation low-pass filter of claim 1 to 8 any one, the frequency mixer is connected with the simulation low-pass filter, described
Simulation low-pass filter is connected with the sampler;
The frequency mixer, for initial signal to be mixed with random sequence signal, obtains mixed frequency signal;
The simulation low-pass filter, for being filtered to the mixed frequency signal, obtains filtering signal;
The sampler, for being sampled to the filtering signal.
10. a kind of simulation low-pass filter, it is characterised in that including:
Processor;
Memory;And COM1;
Wherein, the processor is used for the instruction for performing the memory storage, to perform following steps in execute instruction:
Received by the COM1 come the mixed frequency signal of self-mixing device, the mixed frequency signal is initial signal and random sequence
Signal after signal mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped with the signal after weighting and obtains composite signal;
The delay of unit interval is carried out to the composite signal, and the delay of unit interval is carried out to the signal after the weighting;
The signal after processing obtains the weighting is weighted to the signal by delay using loop cycle matrix;It is described
The parameter of loop cycle matrix is obtained according to the coefficient of the frequency domain impulse response function of the simulation low-pass filter, the frequency domain
The coefficient of impulse response function meets following condition:The measurement square obtained according to the frequency domain impulse response function and sampling function
Any two row of battle array are uncorrelated;
Signal after delay is input to by the sampler being connected with the simulation low-pass filter by the COM1.
11. simulation low-pass filter according to claim 10, it is characterised in that in the frequency domain impulse response letter at j moment
Number Hj(z) it is:
Wherein, i be the moment numbering, T be the loop cycle matrix cycle, N for A (t) row vector or column vector number,
λ′k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,jFor Ψ
(i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
12. simulation low-pass filter according to claim 11, it is characterised in that the calculation matrix any two arranges not phase
Pass is specifically represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;ΦiFor D
(z)Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to Fourier transformation;FΦj
=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment j, F is
Refer to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F Φj||2For
Seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
13. simulation low-pass filter according to claim 10, it is characterised in that the condition also includes:The pole of system
Point is in unit circle.
14. simulation low-pass filter according to claim 10, it is characterised in that the condition also includes:System pole
More than or equal to preset value.
15. simulation low-pass filter according to claim 10, it is characterised in that the condition also includes:The cycle
The parameter of circular matrix is within a preset range.
16. a kind of filtering method, it is characterised in that methods described includes:
Simulation low-pass filter receives the mixed frequency signal for carrying out self-mixing device, and the mixed frequency signal is that initial signal is believed with random sequence
Signal after number mixing, the frequency mixer is connected with simulation low-pass filter;
The mixed frequency signal is overlapped and obtains composite signal by the simulation low-pass filter with the signal after weighting;
The simulation low-pass filter carries out the delay of unit interval to the composite signal, and the signal after the weighting is entered
The delay of row unit interval;
The simulation low-pass filter is weighted processing to the signal by delay using loop cycle matrix and obtains institute
State the signal after weighting;The parameter of the loop cycle matrix is according to the frequency domain impulse response function of the simulation low-pass filter
Coefficient obtain, the coefficient of the frequency domain impulse response function meets following condition:According to the frequency domain impulse response function and
Any two row for the calculation matrix that sampling function is obtained are uncorrelated;
Signal after delay is input to the sampler being connected with the simulation low-pass filter by the simulation low-pass filter.
17. filtering method according to claim 16, it is characterised in that in the frequency domain impulse response function H at j momentj(z)
For:
Wherein, i be the moment numbering, T be the loop cycle matrix cycle, N for A (t) row vector or column vector number,
λ′k,i,jFor Ψ (T, 0) k-th of characteristic value, λ "k,i,jFor Ψ (i-1,0) Ψ (T, k-th of characteristic value j), λ " 'k,i,jFor Ψ
(i-1, k-th of characteristic value j);
Wherein A (t) is loop cycle matrix.
18. filtering method according to claim 17, it is characterised in that any two row of calculation matrix are uncorrelated specific
Represented with equation below:
Wherein, F Φi=D (z) Hi(z), Hi(z) it is the frequency domain impulse response function at the i moment, D (z) is sampling function;ΦiFor D
(z)Hi(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment i, F refer to Fourier transformation;FΦj
=D (z) Hj(z), ΦjFor D (z) Hj(z) function after Fourier transformation, that is, the corresponding calculation matrix of moment j, F is
Refer to Fourier transformation;(FΦi)HFor to F ΦiConjugate transposition is sought, | | F Φi||2To seek F ΦiMould 2 norms, | | F Φj||2For
Seek F ΦjMould 2 norms, the δ be waviness tolerance value, the VlFor calculation matrix F ΦjIt is any two row.
19. filtering method according to claim 16, it is characterised in that the condition also includes:The limit of system is in list
In circle of position.
20. filtering method according to claim 16, it is characterised in that the condition also includes:System pole be more than or
Equal to preset value.
21. filtering method according to claim 16, it is characterised in that the condition also includes:The loop cycle square
The parameter of battle array is within a preset range.
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