CN106209112A - A kind of self-adapting reconstruction method of translation semigroups compression sampling - Google Patents

Abstract

The invention discloses the self-adapting reconstruction method of a kind of translation semigroups compression sampling, including step: S1, structure translation semigroups compression sampling system carry out multi-channel sampling to input time varying signal, obtain the sampled data of each passage；S2, sampled data is input in learning machine, utilizes study mechanism that sampled data is trained, it is thus achieved that input signal space belonging to time varying signal；S3, according to obtain signal space Automatic adjusument reconfigurable filter realize input time varying signal reconstruct.The present invention, compared with traditional translation semigroups compression sampling reconstructing method, has introduced Automatic adjusument mechanism, it is achieved that the reconstruct of time varying signal；Need not translation semigroups compression sampling system is added additional circuit, it is to avoid the introducing of extra error, decrease hardware spending.

Description

A kind of self-adapting reconstruction method of translation semigroups compression sampling

Technical field

The invention belongs to high-speed, high precision Sampling techniques field, specifically, relate to a kind of translation semigroups compression The self-adapting reconstruction method of sampling.

Background technology

Along with development and the application of communication technology, occur in that technical system is more novel, the signal of the more complicated transition of feature.For Adapt to the collection of these sophisticated signals, it is proposed that the sampling theory of a kind of translation semigroups.This sample mode first with Known signal space approaches input signal, then selects sample space to sample input signal, finally utilizes signal empty Between with the dependency of sample space, input signal is transformed into signal space from sample space, it is achieved reconstruct.By this translation Invariant space sampling theory overcomes traditional sampling theorem and requires the sample frequency shortcoming higher than signal peak frequency twice, completes Collection to signals such as non-limit band, ultra broadband, complexity transitions.

Along with compression theory appearance mathematically, it is proposed that the concept of compression sampling i.e. utilizes p measured value reconstruct long Degree is m (p < m) vector；And by the application of compression sampling theory and finite dimension signal space.By translation semigroups sampling reason Opinion and compression sampling combine and define translation semigroups compression sampling mode, provide a kind of effective for instantaneous many varying signals Sample mode.

But existing translation semigroups compression sampling mode, needs translation semigroups compression sampling system is added volume External circuit, thus has the introducing of extra error, increases hardware spending.

Summary of the invention

For solving the problems referred to above, it is an object of the invention to provide the self adaptation weight of a kind of translation semigroups compression sampling Structure method, is reconstructed into purpose with realize instantaneous changeable signal sampling.

To achieve these goals, the technical solution used in the present invention is as follows:

The self-adapting reconstruction method of a kind of translation semigroups compression sampling, comprises the steps:

S1, structure translation semigroups compression sampling system carry out multi-channel sampling to input time varying signal, obtain each The sampled data of passage；

S2, sampled data is input in learning machine, utilizes study mechanism that sampled data is trained, it is thus achieved that during input Signal space belonging to varying signal；

S3, according to obtain signal space Automatic adjusument reconfigurable filter realize input time varying signal reconstruct.

Specifically, described translation semigroups compression sampling system includes that multiple parallel and input receives input time-varying The resolution filter of signal, the digital to analog converter that input is connected with the outfan of each described resolution filter, digital-to-analogue conversion The outfan of device is connected with the input of learning machine.

Further, in step S1, the model of input time varying signal is:

Wherein,It is translation semigroups V_jGenerating function, C_j[n] is translation semigroups V_jWeight coefficient, Z Represent integer set；Described input time varying signal x (t) ∈ W, wherein, W is signal space, and the generating function of W isK=r, λ_m∈ { 0,1, L, r-1}.

In step S1, the compression sampling model of translation semigroups compression sampling system is: d_i[n]=＜ x (t), s_i(t- nT_s) ＞ i=0,1, L, L-1, wherein s_i(-t) is the sampling of translation semigroups compression sampling system the i-th channel decomposition wave filter Function, T_sFor the sampling period of system, L is the port number of system.

Further, in described step S2, study mechanism utilizes orthogonal Matching pursuitalgorithm, by translation semigroups pressure The sampled data of each passage of contracting sampling obtains the signal space belonging to input signal in real time；Described orthogonal matched jamming is calculated The calculating process of method is as follows:

S201, first acquisition sampling matrix T (ω), sampling equation D (ω)=T (ω) C (ω)；

S202, each row of sampling matrix T (ω) are standardized, it is thus achieved that a new matrix H (ω)；

The row most preferably mated with sampling equation D (ω) in S203, searching matrix H (ω)So thatFor square Battle array H (ω) meets maximumRow；

S204, definition I₀={ λ₀,Then sampling equation D (ω) is projected toOn, remaining Residual volume be R¹D(ω)；

S205, again find in matrix H (ω) with residual volume R¹The row of D (ω) most preferably coupling

S206, make I₁=I₀U{λ₁,By residual volume R¹D (ω) projects toOn, remaining Up-to-date residual volume be expressed as R²D(ω)；

S207, the most constantly it is iterated.

In described step S207, work as I_k-1=I_k-2U{λ_k-1,Work as I_k-1Element Number k meets:

Or R^k-1D (ω)=0

Time, orthogonal Matching pursuitalgorithm stops, and spark (H (ω)) is the degree of rarefication of matrix H (ω),Round under expression.

Yet further, the port number L of described translation semigroups compression sampling system is less than signal space generating function During number r, input time varying signal can be by the compression sampling data reconstruction of translation semigroups compression sampling system.

In described step S3, Automatic adjusument Moore-Penrose is inverse for signal space, it is achieved the weight of input time varying signal Structure, specifically comprises the following steps that

S301, from sampling matrix T (ω) extract λ₀, λ₁, L, λ_k-1Column element constitutes a submatrix τ (ω), now Submatrix τ (ω) is for most preferably mating matrix；

If C (ω) meets | | C (ω) | |₀＜ spark (T (ω))/2, then can be deformed into following formula by sampling equation D (ω) Shown in:

D (ω)=τ (ω) C_s(ω)

Wherein, C_s(ω) it is that C (ω) removes the vector of gained after neutral element；

S302, then utilize the inverse above formula solution of equations that can obtain of Moore-Penrose:

C_s(ω)=(τ (ω)^Hτ(ω))^-1τ(ω)^HD(ω)。

The invention have the benefit that

(1) present invention is the reconstruct for instantaneous many varying signals of the translation semigroups compression sampling self-adapting reconstruction method； Sampled data is trained by available study mechanism, obtains input signal space belonging to time varying signal；Then utilize The inverse reconstruct realizing input time varying signal of Moore-Penrose, it is not necessary to actual filtering interpolation circuit, it is ensured that the standard of reconstruct Really property；Self-adapting reconstruction method can regulate reconfigurable filter in real time according to the signal space judged, adapts to instantaneous many varying signals Reconstruct.

(2) present invention has introduced Automatic adjusument mechanism, it is not necessary to translation semigroups compression sampling system is added volume External circuit, it is to avoid the introducing of extra error, decreases hardware spending.

Accompanying drawing explanation

Fig. 1 is the present invention-translation semigroups compression sampling self-adapting reconstruction block diagram.

Fig. 2 is the present invention-self-adapting reconstruction filter construction block diagram.

Fig. 3 is that Frequency Hopping Signal is sampled by the present invention-translation semigroups compression sampling system, then utilizes self adaptation The waveform that method is reconstructed.

Detailed description of the invention

The invention will be further described with embodiment below in conjunction with the accompanying drawings.Embodiments of the present invention include but not limited to The following example.

Embodiment

As it is shown in figure 1, the system of the self-adapting reconstruction method of a kind of translation semigroups compression sampling, including translation invariant Space compression sampling system, learning machine and self-adapting reconstruction wave filter, the outfan of translation semigroups compression sampling system Being connected with the input of learning machine, the outfan of learning machine is connected with self-adapting reconstruction filter input end.

Wherein, translation semigroups compression sampling system includes that multiple parallel and input receives time varying signal x (t) Resolution filter, the digital to analog converter that input is connected with the outfan of each resolution filter, the outfan of digital to analog converter It is connected with the input of learning machine.

Translation semigroups compression sampling system operating frequency is set as f_x.By translation semigroups compression sampling system Sampling input time varying signal x (t), each passage takes N=32 sampled data, by each channel sampled data d_i=d_i [0], d_i[1], L, d_i[N-1] i=0,1, L, L-1 are input in learning machine, utilize orthogonal Matching pursuitalgorithm to adopt each passage Sample data are trained, and then obtain the signal space belonging to input signal.Then according to acquired signal space self adaptation Regulation reconfigurable filter realizes the reconstruct of signal.

According to translation semigroups compression sampling structure, translation semigroups compression sampling system can represent in a frequency domain For:

T (ω) C (ω)=D (ω)

In formula,

$T\left(\mathrm{\&omega;}\right)=\left(\begin{array}{cccc}{t}_0\left(\mathrm{\&omega;}\right)& t_1\left(\mathrm{\&omega;}\right)& L& t_{r-1}\left(\mathrm{\&omega;}\right)\end{array}\right)=\left(\begin{array}{cccc}{t}_{0,0}\left(\mathrm{\&omega;}\right)& t_{0,1}\left(\mathrm{\&omega;}\right)& L& t_{0,r-1}\left(\mathrm{\&omega;}\right)\\ t_{1,0}\left(\mathrm{\&omega;}\right)& t_{1,1}\left(\mathrm{\&omega;}\right)& L& t_{1,r-1}\left(\mathrm{\&omega;}\right)\\ M& M& O& M\\ t_{L-1,0}\left(\mathrm{\&omega;}\right)& t_{L-1,1}\left(\mathrm{\&omega;}\right)& L& t_{L-1,r-1}\left(\mathrm{\&omega;}\right)\end{array}\right)$

t_j(ω)=(t_0,j(ω) t_1,j(ω) L t_L-1,j(ω))

$t_{i,j}\left(\mathrm{\&omega;}\right)=\underset{n=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{S}_i(\mathrm{\&omega;}+2\mathrm{\&pi;}n){\mathrm{\&psi;}}_j(\mathrm{\&omega;}+2\mathrm{\&pi;}n)$

D (ω)=(D₀(ω) D₁(ω) L D_L-1(ω))^T

C (ω)=(C₀(ω) C₁(ω) L C_r-1(ω))^T

s_i(ω) it is resolution filter s_iThe Fourier transform of (-t)；C_j(ω) it is discrete series C_jThe Fourier of [n] becomes Change；ψ_j(ω) representFourier transform continuously；D_i(ω) it is discrete series d_iThe Fourier transform of [n].

Now, equation T (ω) C (ω)=D (ω) can be referred to as equation of sampling, matrix T (ω) is referred to as sampling matrix.

Orthogonal Matching pursuitalgorithm in study mechanism is as follows:

First each row of sampling matrix T (ω) are standardized, the new matrix obtained:

H (ω)=[h₀(ω), h₁(ω), L, h_r-1(ω)]

Wherein, h_j(ω)=t_j(ω)/||t_j(ω)||₂=(t_0,j(ω) t_1,j(ω) L t_L-1,j(ω)) /||t_j (ω)||₂；

Then the row most preferably mated in matrix H (ω) are found with D (ω)MakeFor matrix H (ω) In meet maximumRow, it may be assumed that

${\mathrm{\&lambda;}}_0=\arg \underset{i}{max}\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}\left|h_i^H\left(\mathrm{\&omega;}\right)D\left(\mathrm{\&omega;}\right)\right|d\mathrm{\&omega;}$

Definition I₀={ λ₀,Then D (ω) is projected toOn, remaining residual volume is R¹D (ω), it is:

$D\left(\mathrm{\&omega;}\right)=P_{V_{{\mathrm{\&lambda;}}_0}}D\left(\mathrm{\&omega;}\right)+R^{1}D\left(\mathrm{\&omega;}\right)$

In formula,Represent that D (ω) existsOn projection.

Then, then find in H (ω) with residual volume R¹The row of D (ω) most preferably couplingMake I₁=I₀U{λ₁,By residual volume R¹D (ω) projects toOn, remaining up-to-date residual volume is expressed as R²D (ω), The most constantly being iterated, kth time iteration is represented by:

$R^{k-1}D\left(\mathrm{\&omega;}\right)=P_{V_{{\mathrm{\&lambda;}}_{k-1}}}{R}^{k-1}D\left(\mathrm{\&omega;}\right)+R^{k}D\left(\mathrm{\&omega;}\right)$

Wherein,

${\mathrm{\&lambda;}}_{k-1}=\arg \underset{i}{max}\frac{1}{2\mathrm{\&pi;}}{\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}\left|h_i^H\left(\mathrm{\&omega;}\right)R^{i-1}D\left(\mathrm{\&omega;}\right)\right|d\mathrm{\&omega;}$

Then I_k-1=I_k-2U{λ_k-1,Work as I_k-1Element number k meet,

Or R^k-1D (ω)=0

Time, optimal Matching pursuitalgorithm stops, and wherein, spark (H (ω)) is the degree of rarefication of matrix H (ω),Under expression Round.

λ is extracted from sampling matrix T (ω)₀, λ₁, L, λ_k-1Column element constitutes a submatrix τ (ω), now submatrix τ (ω) is for most preferably mating matrix, it may be assumed that

$\mathrm{\&tau;}\left(\mathrm{\&omega;}\right)=\&lsqb;t_{{\mathrm{\&lambda;}}_0}\left(\mathrm{\&omega;}\right),t_{{\mathrm{\&lambda;}}_1}\left(\mathrm{\&omega;}\right),L,t_{{\mathrm{\&lambda;}}_{k-1}}\left(\mathrm{\&omega;}\right)\&rsqb;.$

If_C(ω)Meet | | C (ω) | |₀＜ spark (T (ω))/2, then can be deformed into shown in following formula by sampling equation:

τ(ω)C_s(ω)=D (ω)

Wherein C_s(ω) it is that C (ω) removes the vector of gained after neutral element.

Then utilize Moore-Penrose against obtaining above formula solution of equations:

C_s(ω)=(τ (ω)^Hτ(ω))^-1τ(ω)^HD(ω)

And then, utilize translation semigroups compression sampling data to achieve the self-adapting reconstruction of input signal.

The periodically nonuniform sampling system building a L * channel realizes translation semigroups compression sampling, then decompose filtering Device s_iThe Fourier transform of (-t)Wherein_ΔtiFor prolonging of translation semigroups compression sampling system the i-th passage Time the time.Now, sampling matrix is

$\begin{array}{c}T\left(\mathrm{\&omega;}\right)=\left(\begin{array}{cccc}{e}^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{0}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_0/T_s}& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_0/T_s}& L& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{r-1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_0/T_s}\\ e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{0}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_1/T_s}& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_1/T_s}& L& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{r-1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_1/T_s}\\ M& M& O& M\\ e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{0}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_{L-1}/T_s}& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_{L-1}/T_s}& L& e^{j(\mathrm{\&omega;}+{\mathrm{\&beta;}}_{r-1}2\mathrm{\&pi;}){\mathrm{\&Delta;t}}_{L-1}/T_s}\end{array}\right)\\ =\left(\begin{array}{cccc}{e}^{{\mathrm{j\&omega;\&Delta;t}}_0/T_s}& 0& L& 0\\ 0& e^{{\mathrm{j\&omega;\&Delta;t}}_1/T_s}& L& 0\\ M& M& O& M\\ 0& 0& L& e^{{\mathrm{j\&omega;\&Delta;t}}_{L-1}/T_s}\end{array}\right)\left(\begin{array}{cccc}{e}^{{\mathrm{j\&beta;}}_{0}2{\mathrm{\&pi;\&Delta;t}}_0/T_s}& e^{{\mathrm{j\&beta;}}_{1}2{\mathrm{\&pi;\&Delta;t}}_0/T_s}& L& e^{{\mathrm{j\&beta;}}_{r-1}2{\mathrm{\&pi;\&Delta;t}}_0/T_s}\\ e^{{\mathrm{j\&beta;}}_{0}2{\mathrm{\&pi;\&Delta;t}}_1/T_s}& e^{{\mathrm{j\&beta;}}_{1}2{\mathrm{\&pi;\&Delta;t}}_1/T_s}& L& e^{{\mathrm{j\&beta;}}_{r-1}2{\mathrm{\&pi;\&Delta;t}}_1/T_s}\\ M& M& O& M\\ e^{{\mathrm{j\&beta;}}_{0}2{\mathrm{\&pi;\&Delta;t}}_{L-1}/T_s}& e^{{\mathrm{j\&beta;}}_{1}2{\mathrm{\&pi;\&Delta;t}}_{L-1}/T_s}& L& e^{{\mathrm{j\&beta;}}_{r-1}2{\mathrm{\&pi;\&Delta;t}}_{L-1}/T_s}\end{array}\right)\end{array}$

In formula, T_sFor the sampling period of sampling system, 2 π β_iRepresentThe translation semigroups frequency spectrum translation generated To [-π, π) needed for translation number.

And then, it is available from adapting to reconfigurable filter structure as in figure 2 it is shown, sampled data first passes through study mechanism acquisition Set I_k-1, according to I_k-1In the adaptively selected Moore-Penrose of element is inverse and zero interpolation point, it is achieved the weight of input signal Structure.

Fig. 3 show the present invention when Frequency Hopping Signal is sampled by translation semigroups compression sampling system, self adaptation Reconfiguration waveform.Input signal is:

$x\left(t\right)=\left\{\begin{array}{ccc}\cos \left(2{\mathrm{\&pi;f}}_{1}t\right)& 0\&le;t<1.3333\mathrm{\&mu;}s& f_1=3.5\&times;{10}^{7}Hz\\ \cos \left(2{\mathrm{\&pi;f}}_{2}t\right)& 1.3333\mathrm{\&mu;}s\&le;t<2.6667\mathrm{\&mu;}s& f_2={10}^{7}Hz\\ \cos \left(2{\mathrm{\&pi;f}}_{3}t\right)& 2.6667\mathrm{\&mu;}s\&le;t<4\mathrm{\&mu;}s& f_3=8\&times;{10}^{7}Hz\end{array}\right.$

Frequency Hopping Signal.As seen from Figure 3, the reconstructing method that the present invention proposes can realize the heaviest of Frequency Hopping Signal Structure.

According to above-described embodiment, the present invention just can be realized well.What deserves to be explained is, before above-mentioned design principle Put, for solving same technical problem, even if some made on architecture basics disclosed in this invention are without substantial Changing or polishing, the essence of the technical scheme used is still as the present invention, therefore it should also be as the protection model in the present invention Enclose.

Claims (8)

1. the self-adapting reconstruction method of a translation semigroups compression sampling, it is characterised in that comprise the steps:

S1, structure translation semigroups compression sampling system carry out multi-channel sampling to input time varying signal, obtain each passage Sampled data；

S2, sampled data is input in learning machine, utilizes study mechanism that sampled data is trained, it is thus achieved that input time-varying letter Number affiliated signal space；

S3, according to obtain signal space Automatic adjusument reconfigurable filter realize input time varying signal reconstruct.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 1, it is characterised in that Described translation semigroups compression sampling system includes that multiple parallel and input reception input time varying signal decomposition filters Device, the digital to analog converter that input is connected with the outfan of each described resolution filter, the outfan of digital to analog converter and The input of habit machine connects.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 1, it is characterised in that In step S1, the model of input time varying signal is:

Wherein,It is translation semigroups V_jGenerating function, C_j[n] is translation semigroups V_jWeight coefficient, Z table Show integer set；Described input time varying signal x (t) ∈ W, wherein, W is signal space, and the generating function of W isλ_m∈ { 0,1, L, r-1}.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 3, it is characterised in that In step S1, the compression sampling model of translation semigroups compression sampling system is: d_i[n]=< x (t), s_i(t-nT_s) > i=0, 1, L, L-1, wherein s_i(-t) is the sampling function of translation semigroups compression sampling system the i-th channel decomposition wave filter, T_sFor being In the sampling period of system, L is the port number of system.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 4, it is characterised in that In described step S2, study mechanism utilizes orthogonal Matching pursuitalgorithm, by each passage of translation semigroups compression sampling Sampled data obtains the signal space belonging to input signal in real time；The calculating process of described orthogonal Matching pursuitalgorithm is as follows:

S201, first acquisition sampling matrix T (ω), sampling equation D (ω)=T (ω) C (ω)；

S202, each row of sampling matrix T (ω) are standardized, it is thus achieved that a new matrix H (ω)；

The row most preferably mated with sampling equation D (ω) in S203, searching matrix H (ω)MakeFor matrix H (ω) maximum is met inRow；

S204, definition I₀={ λ₀,Then sampling equation D (ω) is projected toOn, remaining remnants Amount is R¹D(ω)；

S205, again find in matrix H (ω) with residual volume R¹The row of D (ω) most preferably coupling

S206, make I₁=I₀U{λ₁,By residual volume R¹D (ω) projects toOn, remaining New residual volume is expressed as R²D(ω)；

S207, the most constantly it is iterated.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 5, it is characterised in that In described step S207, work as I_k-1=I_k-2U{λ_k-1,Work as I_k-1Element number k full Foot:

Or R^k-1D (ω)=0

Time, orthogonal Matching pursuitalgorithm stops, and spark (H (ω)) is the degree of rarefication of matrix H (ω),Round under expression.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 6, it is characterised in that When the port number L of described translation semigroups compression sampling system is less than signal space generating function number r, input time varying signal Can be by the compression sampling data reconstruction of translation semigroups compression sampling system.

The self-adapting reconstruction method of a kind of translation semigroups compression sampling the most according to claim 7, it is characterised in that In described step S3, Automatic adjusument Moore-Penrose is inverse for signal space, it is achieved the reconstruct of input time varying signal, specifically walks Rapid as follows:

S301, from sampling matrix T (ω) extract λ₀, λ₁, L, λ_k-1Column element constitutes a submatrix τ (ω), the most sub-square Battle array τ (ω) is for most preferably mating matrix；

If C (ω) meets | | C (ω) | |₀＜ spark (T (ω))/2, then can be deformed into shown in following formula by sampling equation D (ω):

D (ω)=τ (ω) C_s(ω)

Wherein, C_s(ω) it is that C (ω) removes the vector of gained after neutral element；

S302, then utilize the inverse above formula solution of equations that can obtain of Moore-Penrose:

C_s(ω)=(τ (ω)^Hτ(ω))^-1 τ(ω)^H D(ω)。