CN103269223B - A kind of analog signal compressive sampling method - Google Patents

Abstract

The invention provides a kind of analog signal compressive sampling method, framework basis proposes compression calculation matrix, by to compression sampling value sequence and compression calculation matrix synchronous conversion, remove matrix-vector relational expression correlation on the impact of tested analog signal reconstruction property, finally with this relational expression, tested analog signal is reconstructed, obtains the sample sequence of tested analog signal.Like this, when integrator carries out integration to the signal after demodulation in sampling time section, do not carry out reset processing, solve the incomplete Sampling of signal that integrator causes discharge time, improve the performance of analog information Transpression sampling system.

Description

A kind of analog signal compressive sampling method

Technical field

The invention belongs to high speed preiodic type technical field of signal sampling, more specifically say, relate to a kind of analog signal compressive sampling method that can reduce system difficulty.

Background technology

Compression sampling technology is a kind of lack sampling method based on compressive sensing theory.This technology utilizes the tested analog signal of preiodic type after Fourier transform, a small amount of frequency content is only had to have remarkable amplitude, the amplitude of the frequency content of the overwhelming majority is this sparse characteristic of zero, high speed PRBS is adopted to carry out random demodulation at frequency domain to measured signal, demodulated output signal is compressed with integrator, finally with low speed ADC, the signal after compression is sampled, can accurate reconstruction primary signal and tested analog signal by optimization algorithm.

Existing compression sampling technology realizes principle as shown in Figure 1, and the expression formula of m sampled value y [m] is:

$y\[m\]={\∫}_{(m-1)\·T_s}^{{\mathrm{mT}}_s}x\left(\mathrm{\τ}\right)p_c\left(\mathrm{\τ}\right)d\mathrm{\τ}---\left(1\right)$

In formula, x (t) is tested analog signal, p _ct () is pseudo random sequence, T _sfor the sampling period.

Existing compressive sampling method, is needed after each sample to be resetted to integrator by auxiliary circuit, avoids the information coupling between adjacent double sampling with this, but, adopt auxiliary circuit complicated to integrator reset realizing circuit.And the time needed for each integrator resets is unknown, therefore, must adopt the longer resetting time of a unification when resetting to it.Integrator is in reseting procedure simultaneously, cannot collect, will cause information leakage to the energy of tested analog signal.This impact is presented as the incomplete sampling to tested analog signal in sampled value, will cause the distortion of reconstruction signal when being reconstructed tested analog signal with this sampled value.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of analog signal compressive sampling method is provided, to solve the incomplete sampling effect that integrator causes resetting time, improve the performance of compression sampling signal reconstruction.

For realizing above object, analog signal compressive sampling method of the present invention, is characterized in that, comprise the following steps:

(1), tested analog signal carries out random demodulation with the pseudo random sequence with signal nyquist frequency through frequency mixer, signal after demodulation exports all will carry the spectrum information of signal over the entire frequency band, integrator realizes the compression to signal after demodulation, last to sample to integral output signal far below the sample rate of signal nyquist frequency, obtain compression sampling value sequence;

In sampling time section, when integrator carries out integration to the signal after demodulation, do not carry out reset processing;

(2), according to the mathematics behavior model of compression sampling system, the compression calculation matrix after the synchronous conversion of structure;

(3), the compression sampling value sequence obtained synchronously is converted, according to the compression calculation matrix after the synchronous conversion of structure, obtain the matrix-vector relational expression removing correlation, finally with this relational expression, tested analog signal is reconstructed, obtain the sample sequence of tested analog signal, complete the compression sampling to tested analog signal.

The object of the present invention is achieved like this:

Analog signal compressive sampling method of the present invention, framework basis proposes compression calculation matrix, by to compression sampling value sequence and compression calculation matrix synchronous conversion, remove matrix-vector relational expression correlation on the impact of tested analog signal reconstruction property, finally with this relational expression, tested analog signal is reconstructed, obtains the sample sequence of tested analog signal.Like this, when integrator carries out integration to the signal after demodulation in sampling time section, do not carry out reset processing, solve the incomplete Sampling of signal that integrator causes discharge time, improve the performance of analog information Transpression sampling system.

Accompanying drawing explanation

Fig. 1 is conventional compression sampling principle block diagram;

Fig. 2 is a kind of embodiment theory diagram of analog signal compressive sampling method of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described, so that those skilled in the art understands the present invention better.Requiring particular attention is that, in the following description, when perhaps the detailed description of known function and design can desalinate main contents of the present invention, these are described in and will be left in the basket here.

Fig. 2 is a kind of embodiment theory diagram of analog signal compressive sampling method of the present invention.

As shown in Figure 2, in the present embodiment, analog signal compressive sampling method of the present invention comprises the following steps:

Step ST1: obtain compression sampling value sequence.

Tested analog signal signal x (t) and the pseudo random sequence P with signal nyquist frequency _ct () adopts frequency mixer to carry out random demodulation.In the present embodiment, in order to meet circuit realizability and compressive sensing theory to the requirement compressing calculation matrix, pseudo random sequence P _ct () adopts Rider horse contract pseudo random sequence composition.

Integrator realizes the compression to signal after demodulation, and integrator can adopt voltage integrator to realize.In the present invention, at sampling time section 0 ~ mT _sin, when integrator carries out integration to the signal after demodulation, do not carry out reset processing.This and prior art reset processing, at each sampling period T _scarry out integration difference.

Last to sample to integral output signal far below the sample rate of signal nyquist frequency, obtain.Compared with prior art, the present invention does not need to carry out reset processing to integrator.

Compression sampling value sequence y [m] expression formula is:

$y\[m\]={\∫}_0^{{\mathrm{mT}}_s}x\left(\mathrm{\τ}\right)p_c\left(\mathrm{\τ}\right)d\mathrm{\τ}---\left(2\right)$

Wherein, m=1,2 ..., M, M are compression sampling value sequence length.

Step ST2: the compression calculation matrix Φ after the synchronous conversion of structure.

In the present invention, being functionally equivalent to each sampling period compression sampling value summation of integrator, therefore, the matrix form of integrator can be expressed as:

In formula, Matrix C is that M × N ties up matrix, and q=N/M, N are for treating reconstruction signal length, and in matrix, the element of position of non-1 is 0.When N can not be divided exactly by M, adjacent rows shares the information of a sampled value, and in Matrix C, temporally length ratio relation adopts fraction representation.Such as:

Work as M=3, during N=15, the expression formula of Matrix C is:

$C=\left[\begin{array}{ccccccccccccccc}1& 1& 1& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 0& 0& 0& 0& 0\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\end{array}\right]---\left(4\right)$

Work as M=3, during N=14, the expression formula of Matrix C is:

$C=\left[\begin{array}{cccccccccccccc}1& 1& 1& 1& 2/3& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1/3& 0& 0& 0& 0\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\end{array}\right]---\left(5\right)$

Compression calculation matrix Φ after the synchronous conversion of structure is:

$\mathrm{\Φ}=C^{\′}\·P=\left[\begin{array}{c}{c}_1\\ c_2-c_1\\ .\\ .\\ .\\ c_M-c_{M-1}\end{array}\right]\·P---\left(6\right)$

C in formula ₁c _mfor the row vector of integrator Matrix C, C ' is the integrator matrix after synchronous conversion.P is pseudo random sequence P _ct N × N that () is formed as diagonal element ties up diagonal matrix, if pseudo random sequence is [ε ₁ε ₂ε _n], then vector element ε _ivalue be 1 or-1, and value distribution probability meet: the matrix notation of P is:

In formula, the value of off-diagonal element is 0.

Step ST3: synchronously convert compression sampling value sequence, carries out tested analog signal reconstruct after obtaining the matrix-vector relational expression of removal correlation.

In analog signal compressive sampling method of the present invention, owing to not resetting to integrator, therefore, current compression sampled value contains the information of each sampling period compression sampling value, there is between sampled value very strong correlation, in order to remove the impact of this correlation on compression sampling systematic function, current sample values is adopted to deduct the synchronous conversion of adjacent sample values above.Sampled value sequences y after synchronous conversion and the compression calculation matrix Φ after synchronous conversion have the matrix-vector relational expression removing correlation as follows:

y＝Φx＝Φ·Ψα,(9)

Wherein, y=[y [1] y [2]-y [1] ... y [M]-y [M-1]], in formula, Ψ is that frequency-domain sparse represents base, be made up of discrete Fourier transform (DFT) vector, Ψ is that N × N ties up matrix, α is the sample sequence x waiting to reconstruct tested analog signal represents base Ψ conversion coefficient at frequency-domain sparse, and the sequence length of α and x is N.

By compressed sensing signal reconstruction algorithm, obtain conversion coefficient α, obtain the sample sequence x of tested analog signal x (t) finally by inverse fourier transform.

Tested analog signal is reconstructed and belongs to prior art, do not repeat them here.

The compression sampling value sequence that the present invention proposes with compress calculation matrix and synchronously convert, can correlation be reduced.

Compression calculation matrix coefficient correlation μ (Φ, Ψ) is defined as:

$\mathrm{\&mu;}(\mathrm{\&Phi;},\mathrm{\&Psi;})=\underset{1\&le;i,j\&le;N}{max}\left|<{\mathrm{\&phi;}}_i,{\mathrm{\&psi;}}_j>\right|$

φ in formula _iwith ψ _ji-th row vector of difference matrix Φ and Ψ and a jth column vector.

Convert the probability that front coefficient correlation is less than constant u (u>0) satisfy condition assuming that compression sampling value sequence be synchronous with compression calculation matrix (Φ=CP):

Compression sampling value sequence is synchronous with compression calculation matrix (Φ=C ' P) to be converted the probability that afterwards coefficient correlation is less than constant u and satisfies condition:

P ₁with p ₂for being greater than the normal number of 0, then p ₂>p ₁, that is: after conversion coefficient correlation to be less than the probability of constant u larger.

Prove:

Coefficient correlation μ (Φ, Ψ) before synchronous conversion, due to Φ=CP, so coefficient correlation can be rewritten as μ (CP, Ψ)=μ (C, P Ψ), due to $<c_i,{\mathrm{P\&psi;}}_j>={\mathrm{\&Sigma;}}_{k=1}^N{\mathrm{\&epsiv;}}_k{c}_{ki}^{*}{\mathrm{\&psi;}}_{kj}={\mathrm{\&Sigma;}}_{k=1}^N{\mathrm{\&epsiv;}}_k{a}_k^{ij},$ Here $a_k^{ij}=c_{ki}^{*}{\mathrm{\&psi;}}_{kj},$ ε _kfor a kth diagonal element of matrix P, c _ifor i-th row vector of Matrix C, for the conjugate transpose of row k i-th column element of Matrix C, ψ _kjfor the row k jth column element of matrix Ψ.Following relation is had by Hough fourth inequality:

For all constant u>0,1≤i, j≤N, with associating circle of probability is:

So:

Coefficient correlation μ (Φ, Ψ) after proving by the same methods synchronously converts=μ (C'P, Ψ) meets following condition:

In formula obviously, can obtain according to the definition of Matrix C and C ' $\left|\right|b^{ij}|{|}_2^2<|\left|a^{ij}\right|{|}_2^2.$ Assuming that

$p_1=1-2\underset{1\&le;i,j\&le;N}{\&Sigma;}\exp (-\frac{u^2}{2\left|\right|a^{ij}|{|}_2^2})$

With

$p_2=1-2\underset{1\&le;i,j\&le;N}{\&Sigma;}\exp (-\frac{u^2}{2\left|\right|b^{ij}|{|}_2^2})$

Due to so p ₂>p ₁, that is: after conversion, coefficient correlation is less than the probability of constant u more greatly, can reduce correlation.

Although be described the illustrative embodiment of the present invention above; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various change to limit and in the spirit and scope of the present invention determined, these changes are apparent, and all innovation and creation utilizing the present invention to conceive are all at the row of protection in appended claim.

Claims (3)

1. an analog signal compressive sampling method, is characterized in that, comprises the following steps:

(1), tested analog signal carries out random demodulation with the pseudo random sequence with signal nyquist frequency through frequency mixer, signal after demodulation exports all will carry the spectrum information of signal over the entire frequency band, integrator realizes the compression to signal after demodulation, last to sample to integral output signal far below the sample rate of signal nyquist frequency, obtain compression sampling value sequence;

In sampling time section, when integrator carries out integration to the signal after demodulation, do not carry out reset processing;

(2) the compression calculation matrix, after the synchronous conversion of structure:

$\mathrm{\&Phi;}=C^{\&prime;}\&CenterDot;P=\left[\begin{array}{c}{c}_1\\ c_2-c_1\\ .\\ .\\ .\\ c_M-c_{M-1}\end{array}\right]\&CenterDot;P,$

C in formula ₁c _mfor the row vector of integrator Matrix C, C ' is the integrator matrix after synchronous conversion; P is pseudo random sequence P _ct N × N that () is formed as diagonal element ties up diagonal matrix, and pseudo random sequence is [ε ₁ε ₂ε _n], then vector element ε _ivalue be 1 or-1, and value distribution probability meet: matrix P is:

In formula, the value of off-diagonal element is 0;

Integrator Matrix C is:

In formula, integrator Matrix C is that M × N ties up matrix, and q=N/M, N are for treating reconstruction signal length, and in matrix, the element of position of non-1 is 0; When N can not be divided exactly by M, adjacent rows shares the information of a sampled value, and in integrator Matrix C, temporally length ratio relation adopts fraction representation;

(3), the compression sampling value sequence obtained synchronously is converted, according to the compression calculation matrix after the synchronous conversion of structure, obtain the matrix-vector relational expression removing correlation, finally with this relational expression, tested analog signal is reconstructed, obtain the sample sequence of tested analog signal, complete the compression sampling to tested analog signal.

2. analog signal compressive sampling method according to claim 1, is characterized in that, the pseudo random sequence described in step (1) is Rider horse contract pseudo random sequence.

3. analog signal compressive sampling method according to claim 1, is characterized in that, the matrix-vector relational expression of the removal correlation described in step (3):

y＝Φx＝Φ·Ψα,

Wherein, sampled value sequence y=[y [1] y [2]-y [1] after synchronous conversion ... y [M]-y [M-1]], in formula, Ψ is that frequency-domain sparse represents base, be made up of discrete Fourier transform (DFT) vector, Ψ is that N × N ties up matrix, α is the sample sequence x waiting to reconstruct tested analog signal represents base Ψ conversion coefficient at frequency-domain sparse, and the sequence length of α and x is N.