CN103269223A - Analog signal compressed sampling method - Google Patents

Abstract

The invention provides an analog signal compressed sampling method. The method includes the steps of providing a compression measurement matrix on the basis of a framework, carrying out synchronous transformation on a compression sampling value sequence and the compression measurement matrix, eliminating the influence of correlation of a matrix vector equation on reconstruction performance of detected analog signals, carrying out reconstruction on the detected analog signals according to the equation, and obtaining sampling sequences of the detected analog signals. When an integrator carries out integration on demodulated signals within a sampling time period, the integrator does not carry out restoration processing. Therefore, the analog signal compressed sampling method solves the problem of signal incompletion sampling caused by charging time of the integrator, and improves the performance of an analog information transpression sampling system.

Description

A kind of analog signal compression 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 compression sampling method that can reduce system's design difficulty.

Background technology

The compression sampling technology is a kind of method of sampling of owing based on the compressed sensing theory.This technology utilizes the tested analog signal of preiodic type after Fourier transform, only there is the small number of frequencies composition to have remarkable amplitude, the amplitude of the frequency content of the overwhelming majority is zero this sparse characteristic, adopt the high speed pseudo random sequence at frequency domain demodulation at random to be carried out in measured signal, demodulated output signal is compressed with integrator, with low speed ADC the signal after compressing is sampled at last, can accurately rebuild primary signal by optimization algorithm is tested analog signal.

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

$y\left[m\right]=\∫\begin{array}{c}m{T}_s\\ (m-1)\·T_s\end{array}x\left(\mathrm{\τ}\right)p_c\left(\mathrm{\τ}\right)\mathrm{d\τ}---\left(1\right)$

X in the formula (t) is tested analog signal, p _c(t) be pseudo random sequence, T _sBe the sampling period.

Existing compression sampling method needs by auxiliary circuit integrator to be resetted after each sampling, avoids the information between the adjacent double sampling to be coupled with this, yet, adopt auxiliary circuit that integrator is resetted and realize the circuit complexity.And therefore time the unknown that each integrator resets required, must adopt the long resetting time of a unification when it is resetted.Integrator can't be collected the energy of tested analog signal in reseting procedure simultaneously, will cause information leakage.This influence is presented as in sampled value incomplete sampling to tested analog signal will cause the distortion of reconstruction signal when with this sampled value tested analog signal being reconstructed.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, a kind of analog signal compression 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 purpose, analog signal compression sampling method of the present invention is characterized in that, may further comprise the steps:

(1), tested analog signal is carried out demodulation at random with the pseudo random sequence with signal nyquist frequency through frequency mixer, signal after the demodulation output all will carry the spectrum information of signal on whole frequency band, integrator is realized the compression to signal after the demodulation, last far below the sample rate of signal nyquist frequency integral output signal is sampled, obtain the compression sampling value sequence;

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

(2), according to the mathematics behavior model of compression sampling system, matrix is measured in the compression of constructing after the synchronous conversion;

(3), the compression sampling value sequence that obtains is carried out synchronous conversion, measure matrix according to the compression after the synchronous conversion of structure, obtain removing the matrix-vector relational expression of correlation, with this relational expression tested analog signal is reconstructed at last, obtain the sample sequence of tested analog signal, finish the compression sampling to tested analog signal.

The object of the present invention is achieved like this:

Analog signal compression sampling method of the present invention, propose compression on the framework basis and measured matrix, by the synchronous conversion that matrix is measured in compression sampling value sequence and compression, remove the right tested analog signal reconstruct Effect on Performance of matrix-vector relational expression correlation, with this relational expression tested analog signal is reconstructed at last, obtains the sample sequence of tested analog signal.Like this, when the signal of integrator after to demodulation carries out integration in the sampling time section, do not carry out reset processing, solved signal that integrator the causes discharge time problem of not exclusively sampling, improved the performance of analog information conversion compression sampling system.

Description of drawings

Fig. 1 is conventional compression sampling principle block diagram;

Fig. 2 is a kind of embodiment theory diagram of analog signal compression 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.What need point out especially 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 were described in here and will be left in the basket.

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

As shown in Figure 2, in the present embodiment, analog signal compression sampling method of the present invention may further comprise the steps:

Step ST1: obtain the compression sampling value sequence.

Tested analog signal signal x (t) and the pseudo random sequence P with signal nyquist frequency _c(t) adopt frequency mixer to carry out demodulation at random.In the present embodiment, in order to satisfy the requirement that circuit realizability and compressed sensing theory are measured matrix to compression, pseudo random sequence P _c(t) adopt Rider horse contract pseudo random sequence to form.

Integrator is realized the compression to signal after the demodulation, and integrator can adopt the voltage integrating meter device to realize.In the present invention, at sampling time section 0～mT _sIn, when the signal of integrator after to demodulation carries out integration, do not carry out reset processing.This and prior art reset processing are at each sampling period T _sCarry out the integration difference.

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

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

$y\left[m\right]=\∫\begin{array}{c}m{T}_s\\ 0\end{array}x\left(\mathrm{\τ}\right)p_c\left(\mathrm{\τ}\right)\mathrm{d\τ}---\left(2\right)$

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

Step ST2: matrix Φ is measured in the compression of constructing after the synchronous conversion.

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

In the formula, Matrix C is that M * N ties up matrix, q=N/M, and N is for treating reconstruction signal length, the element of non-1 position is 0 in the matrix.When N can not be divided exactly by M, adjacent two row were shared the information of a sampled value, in Matrix C, adopted fraction representation by time length ratio relation.For example:

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:

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

Matrix Φ is measured in compression after the synchronous conversion of structure:

$\mathrm{\&Phi;}=C^{\&prime;}\&CenterDot;P=\left[\begin{array}{c}{c}_1\\ c_2-{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00003135205000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_M-c_{M-1}\end{array}\right]\&CenterDot;P---\left(6\right)$

C in the formula ₁C _MBe the row vector of integrator Matrix C, C ' is the integrator matrix after the synchronous conversion.P is pseudo random sequence P _c(t) N * N that constitutes as diagonal element ties up diagonal matrix, if pseudo random sequence is [ε ₁ε ₂ε _N], vector element ε then _iValue be 1 or-1, and the probability that value distributes satisfies:

The matrix notation of P is:

The value of off-diagonal element is 0 in the formula.

Step ST3: the compression sampling value sequence is carried out synchronous conversion, carry out tested analog signal reconstruct after obtaining removing the matrix-vector relational expression of correlation.

In the analog signal compression sampling method of the present invention, owing to integrator is not resetted, therefore, current compression sampling value has comprised the information of each sampling period compression sampling value, has very strong correlation between the sampled value, in order to remove this correlation to the influence of compression sampling systematic function, adopt current sampled value to deduct the synchronous conversion of front neighbouring sample value.The matrix-vector relational expression that matrix Φ has following removal correlation is measured in compression after sampled value sequence y after the conversion synchronously and the conversion synchronously:

y=Φx=Φ·Ψα, (9)

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

By compression transducing signal restructing algorithm, obtain conversion coefficient α, obtain the sample sequence x of tested analog signal x (t) at last by inverse fourier transform.

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

The compression sampling value sequence that the present invention proposes is measured the synchronous conversion of matrix with compression, can reduce correlation.

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

$\mathrm{\&mu;}(\mathrm{\&Phi;},\mathrm{\&Psi;})=\underset{1\&le;i,j\&le;N}{\mathrm{<figure-callout\; id="1"\; label="max"\; filenames="HDA00003135205000012.png"\; state="\{\{state\}\}">max</figure-callout>}}|\&lang;{\mathrm{\&phi;}}_i,{\mathrm{\&psi;}}_j\&rang;|$

φ in the formula _iWith ψ _jJ column vector of i capable vector sum of difference matrix Φ and Ψ.

Suppose that compression sampling value sequence and compression measure the probability of matrix (coefficient correlation is less than constant u(u before the conversion synchronously of Φ=CP)〉0) and satisfy condition:

Compression sampling value sequence and compression measure matrix (coefficient correlation satisfies condition less than the probability of constant u after the conversion synchronously of Φ=C ' P):

p ₁With p ₂For greater than 0 positive constant, then p ₂P ₁, that is: coefficient correlation is bigger less than the probability of constant u after the conversion.

Proof:

Synchronously coefficient correlation μ before the conversion (Φ, Ψ) because Φ=CP, thus coefficient correlation can be rewritten as μ (CP, Ψ)=μ (C, P Ψ) because $\&lang;c_i,P{\mathrm{\&psi;}}_j\&rang;={\mathrm{\&Sigma;}}_{k=1}^N{\mathrm{\&epsiv;}}_k{c}_{\mathrm{ki}}^{*}{\mathrm{\&psi;}}_{\mathrm{kj}}={\mathrm{\&Sigma;}}_{k=1}^N{\mathrm{\&epsiv;}}_k{a}_k^{\mathrm{ij}},$ Here $a_k^{\mathrm{ij}}=c_{\mathrm{ki}}^{*}{\mathrm{\&psi;}}_{\mathrm{kj}},$ ε _kBe k the diagonal element of matrix P, c _iBe i row vector of Matrix C,

Be the conjugate transpose of the capable i column element of k of Matrix C, ψ _KjThe capable j column element of k for matrix Ψ.By Hough fourth inequality following relation is arranged:

For all constant u〉0,1≤i, j≤N, with

Associating circle of probability is:

So:

In like manner can demonstrate,prove coefficient correlation μ after the synchronous conversion (Φ, Ψ)=μ (C'P, Ψ) satisfy following condition:

In the formula

Obviously, the definition according to Matrix C and C ' can get ${\left|\right|b^{\mathrm{ij}}\left|\right|}_2^2<{\left|\right|a^{\mathrm{ij}}\left|\right|}_2^2.$ Suppose

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00003135205000012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1=1-2\underset{1\&le;i,j\&le;N}{\mathrm{\&Sigma;}}\exp (-\frac{u^2}{2{\left|\right|a^{\mathrm{ij}}\left|\right|}_2^2})$

With

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

Because

So p ₂P ₁, that is: coefficient correlation is bigger less than the probability of constant u after the conversion, can reduce correlation.

Although above the illustrative embodiment of the present invention is described; 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 variations appended claim limit and the spirit and scope of the present invention determined in, these variations are apparent, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (4)

1. an analog signal compression sampling method is characterized in that, may further comprise the steps:

(1), tested analog signal is carried out demodulation at random with the pseudo random sequence with signal nyquist frequency through frequency mixer, signal after the demodulation output all will carry the spectrum information of signal on whole frequency band, integrator is realized the compression to signal after the demodulation, last far below the sample rate of signal nyquist frequency integral output signal is sampled, obtain the compression sampling value sequence;

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

(2), according to the mathematics behavior model of compression sampling system, matrix is measured in the compression of constructing after the synchronous conversion;

(3), the compression sampling value sequence that obtains is carried out synchronous conversion, measure matrix according to the compression after the synchronous conversion of structure, obtain removing the matrix-vector relational expression of correlation, with this relational expression tested analog signal is reconstructed at last, obtain the sample sequence of tested analog signal, finish the compression sampling to tested analog signal.

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

3. analog signal compression sampling method according to claim 2 is characterized in that, the compression described in the step (2) is measured matrix and is:

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

C in the formula ₁C _MBe the row vector of integrator Matrix C, C ' is the integrator matrix after the synchronous conversion; P is pseudo random sequence P _c(t) N * N that constitutes as diagonal element ties up diagonal matrix, if pseudo random sequence is [ε ₁ε ₂ε _N], vector element ε then _iValue be 1 or-1, and the probability that value distributes satisfies:

The matrix notation of P is:

The value of off-diagonal element is 0 in the formula;

The integrator Matrix C can be expressed as:

In the formula, Matrix C is that M * N ties up matrix, q=N/M, and N is for treating reconstruction signal length, the element of non-1 position is 0 in the matrix; When N can not be divided exactly by M, adjacent two row were shared the information of a sampled value, in Matrix C, adopted fraction representation by time length ratio relation.

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

y=Φx=Φ·Ψα,

Wherein, sampled value sequence y=[y[1 after the conversion synchronously] y[2]-y[1] ... y[M]-y[M-1]], Ψ is that frequency-domain sparse is represented base in the formula, constituted by the discrete Fourier transform (DFT) vector, Ψ is that N * N ties up matrix, to be the sample sequence x that treats the tested analog signal of reconstruct represent the conversion coefficient of basic Ψ at frequency-domain sparse to α, and the sequence length of α and x is N.

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