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

Self-adaptive reconstruction method for translation invariant space compression sampling

Technical Field

The invention belongs to the technical field of high-speed and high-precision sampling, and particularly relates to a self-adaptive reconstruction method for translation invariant space compression sampling.

Background

With the development and application of communication technology, signals with more novel technical systems and more complex and transient characteristics appear. In order to adapt to the acquisition of the complex signals, a translation-invariant spatial sampling theory is provided. The sampling mode firstly approximates an input signal by using a known signal space, then selects a sampling space to sample the input signal, and finally converts the input signal from the sampling space to the signal space by using the correlation between the signal space and the sampling space to realize reconstruction. The translation invariant space sampling theory overcomes the defect that the traditional sampling theorem requires the sampling frequency to be higher than twice of the maximum frequency of the signal, and completes the acquisition of signals such as an infinite band, an ultra wide band, complex transient and the like.

With the advent of compression theory mathematically, the concept of compressed sampling has been proposed, namely using p measurements to reconstruct a vector of length m (p < m); and apply compressive sampling theory to a finite dimensional signal space. The translation invariant space sampling theory and the compression sampling are combined to form a translation invariant space compression sampling mode, and an effective sampling mode is provided for transient variable signals.

However, in the conventional translation invariant space compression sampling mode, an additional circuit needs to be added to the translation invariant space compression sampling system, so that an additional error is introduced, and hardware overhead is increased.

Disclosure of Invention

To solve the above problems, an object of the present invention is to provide an adaptive reconstruction method for translational invariant spatial compression sampling, so as to achieve reconstruction of temporally variable signal samples.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a self-adaptive reconstruction method for translation invariant space compression sampling comprises the following steps:

s1, constructing a translation invariant space compression sampling system to perform multi-channel sampling on the input time-varying signal to obtain sampling data of each channel;

s2, inputting the sampling data into a learning machine, training the sampling data by utilizing a learning mechanism, and obtaining a signal space to which the input time-varying signal belongs;

and S3, adaptively adjusting the reconstruction filter according to the obtained signal space to realize the reconstruction of the input time-varying signal.

Specifically, the translation invariant space compression sampling system comprises a plurality of parallel decomposition filters, an input end of each decomposition filter receives an input time-varying signal, a digital-to-analog converter, an output end of each digital-to-analog converter is connected with an input end of a learning machine, and an output end of each digital-to-analog converter is connected with an output end of each decomposition filter.

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

wherein,is a translation invariant space V_jGenerating function of C_j[n]For translation to a constant space V_jZ represents a set of integers, said input time varying signal x (t) ∈ W, where W is the signal space and the generating function of W isk＝r，λ_m∈{0，1，L，r-1}。

In step S1, the compressive sampling model of the translational invariant space compressive sampling system is: d_i[n]＝＜x(t)，s_i(t-nT_s) > i ═ 0,1, L, L-1, where s_i(-T) is the sampling function of the ith channel decomposition filter of the translation invariant space compression sampling system, T_sAnd L is the sampling period of the system, and the number of channels of the system.

Further, in the step S2, the learning mechanism uses an orthogonal matching and tracking algorithm to obtain, in real time, a signal space to which the input signal belongs from the sample data of each channel of the translation invariant space compression sampling; the calculation process of the orthogonal matching tracking algorithm is as follows:

s201, first, obtaining a sampling matrix T (ω), where a sampling equation D (ω) is T (ω) C (ω);

s202, standardizing each column of the sampling matrix T (omega) to obtain a new matrix H (omega);

s203, searching the column which is best matched with the sampling equation D (omega) in the matrix H (omega)So thatFor the maximum value satisfied in the matrix H (omega)A column of (1);

s204, definition I₀＝{λ₀}，Then the sampling equation D (ω) is projected toAbove, the remaining residual amount is R¹D(ω)；

S205, searching the neutralization residue R in the matrix H (omega)¹Best matched column of D (omega)

S206, order I₁＝I₀U{λ₁}，The residual amount R¹D (omega) projection toThe last residual remaining is denoted as R²D(ω)；

And S207, continuously iterating according to the process.

In the step S207, when I_k-1＝I_k-2U{λ_k-1}，When I is_k-1The number k of the elements satisfies:

or R^k-1D(ω)＝0

Then, the orthogonal matching tracking algorithm is stopped, spark (H (omega)) is the sparsity of the matrix H (omega),indicating a lower rounding.

And when the number L of channels of the translation invariant space compression sampling system is less than the number r of signal space generating functions, the input time-varying signal can be reconstructed by the compression sampling data of the translation invariant space compression sampling system.

In step S3, the Moore-Penrose inverse is adaptively adjusted in signal space to realize reconstruction of the input time-varying signal, and the specific steps are as follows:

s301, extracting the lambda-th signal from the sampling matrix T (omega)₀，λ₁，L，λ_k-1The column elements form a sub-matrix tau (omega), and the sub-matrix tau (omega) is an optimal matching matrix;

if C (omega) satisfies | | C (omega) | non-woven gas₀< spark (T (ω))/2, then the sampling equation D (ω) can be transformed as shown below:

D(ω)＝τ(ω)C_s(ω)

wherein, C_s(ω) is a vector obtained by removing zero elements from C (ω);

s302, then using Moore-Penrose inverse, the solution of the equation set of the above formula can be obtained:

C_s(ω)＝(τ(ω)^Hτ(ω))^-1τ(ω)^HD(ω)。

the invention has the beneficial effects that:

(1) the invention relates to a translation invariant space compression sampling self-adaptive reconstruction method aiming at the reconstruction of transient and variable signals; training the sampling data by utilizing a learning mechanism to obtain a signal space to which the input time-varying signal belongs; then, the Moore-Penrose inverse is utilized to realize the reconstruction of the input time-varying signal, an actual interpolation filter circuit is not needed, and the reconstruction accuracy is ensured; the self-adaptive reconstruction method can adjust the reconstruction filter in real time according to the judged signal space, and is suitable for the reconstruction of the instantaneously changeable signals.

(2) The invention introduces a self-adaptive adjusting mechanism, does not need to add an additional circuit to the translation invariant space compression sampling system, avoids the introduction of additional errors and reduces the hardware overhead.

Drawings

FIG. 1 is a block diagram of the present invention, translational invariant spatial compressive sampling adaptive reconstruction.

Fig. 2 is a block diagram of an adaptive reconstruction filter according to the present invention.

Fig. 3 is a waveform obtained by sampling a frequency hopping signal and then reconstructing the frequency hopping signal by using an adaptive method according to the translational invariant space compression sampling system of the present invention.

Detailed Description

The invention is further illustrated by the following figures and examples. Embodiments of the present invention include, but are not limited to, the following examples.

Examples

As shown in fig. 1, a system of an adaptive reconstruction method for translational invariant space compressive sampling includes a translational invariant space compressive sampling system, a learning machine, and an adaptive reconstruction filter, where an output end of the translational invariant space compressive sampling system is connected to an input end of the learning machine, and an output end of the learning machine is connected to an input end of the adaptive reconstruction filter.

The translation invariant space compression sampling system comprises a plurality of parallel decomposition filters of which the input ends receive time-varying signals x (t), a digital-to-analog converter of which the input end is connected with the output end of each decomposition filter, and the output end of the digital-to-analog converter is connected with the input end of a learning machine.

Setting the working frequency of the translation invariant space compression sampling system as f_x. Sampling an input time-varying signal x (t) by a translation invariant space compression sampling system, taking N as 32 sampling data for each channel, and sampling data d of each channel_i＝d_i[0]，d_i[1]，L，d_i[N-1]And (3) inputting the i-0, 1, L, L-1 into a learning machine, training the sampling data of each channel by using an orthogonal matching tracking algorithm, and further acquiring the signal space to which the input signal belongs. And then, adaptively adjusting a reconstruction filter according to the acquired signal space to realize signal reconstruction.

According to the shift-invariant spatial compressive sampling structure, the shift-invariant spatial compressive sampling system can be represented in the frequency domain as:

T(ω)C(ω)＝D(ω)

in the 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) is a decomposition filter s_iFourier transform of (-t); c_j(ω) is a discrete sequence C_j[n]A Fourier transform of (1); psi_j(ω) representsContinuous Fourier transform; d_i(ω) is a discrete sequence d_i[n]The fourier transform of (d).

At this time, equation T (ω) C (ω) ═ D (ω) may be referred to as a sampling equation, and matrix T (ω) may be referred to as a sampling matrix.

The orthogonal matching tracking algorithm in the learning mechanism is as follows:

first, the columns of the sampling matrix T (ω) are normalized, and a new matrix is obtained:

H(ω)＝[h₀(ω)，h₁(ω)，L，h_r-1(ω)]

wherein h is_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 find the best matching column in matrix H (omega) with D (omega)So thatFor the maximum value satisfied in the matrix H (omega)The columns of (1), namely:

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

definition I₀＝{λ₀}，Then projecting D (omega) toAbove, the remaining residual amount is R¹D (ω), i.e.:

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

in the formula,denotes D (ω) is inProjection of (2).

Then, the neutralization residue R in H (omega) is searched¹Best matched column of D (omega)Let I₁＝I₀U{λ₁}，The residual amount R¹D (omega) projection toThe last residual remaining is denoted as R²D (ω), which is continuously iterated according to the above process, and the k-th iteration can be represented as:

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

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}，When I is_k-1The number k of the elements of (a) satisfies,

or R^k-1D(ω)＝0

Then the best match tracking algorithm stops, where spark (H (ω)) is the sparsity of matrix H (ω),indicating a lower rounding.

Extracting the lambda-th from the sampling matrix T (omega)₀，λ₁，L，λ_k-1The column elements form a sub-matrix τ (ω), where the sub-matrix τ (ω) is the best match matrix, i.e.:

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

if it is not_C(ω)Satisfy | | C (omega) | non-woven gas₀< spark (T (ω))/2, the sampling equation can be transformed as shown below:

τ(ω)C_s(ω)＝D(ω)

wherein C is_sAnd (ω) is a vector obtained by removing zero elements from C (ω).

The Moore-Penrose inverse is then used to obtain a solution to the equation set above:

C_s(ω)＝(τ(ω)^Hτ(ω))^-1τ(ω)^HD(ω)

furthermore, the translation invariant space compression sampling data is utilized to realize the self-adaptive reconstruction of the input signal.

Constructing a periodic non-uniform sampling system of L channel to realize translation invariant space compression sampling, and then decomposing the filter s_iFourier transform of (-t)Wherein_ΔtiAnd compressing the delay time of the ith channel of the sampling system for the translation invariant space. At this time, the 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 the formula, T_sFor the sampling period of the sampling system, 2 π β_iTo representThe generated translation-invariant spatial spectrum is translated to the required translation number of [ -pi, pi).

Further, an adaptive reconstruction filter structure can be obtained as shown in fig. 2, the sampled data is first acquired into a set I through a learning mechanism_k-1According to I_k-1The Moore-Penrose inverse and zero interpolation point are adaptively selected by the elements in the (A), so that the reconstruction of the input signal is realized.

Fig. 3 shows the adaptive reconstruction of the waveform when the shift-invariant spatial compression sampling system samples the frequency hopping signal according to the present invention. The input signals are:

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

the frequency hopping signal of (1). As can be seen from fig. 3, the reconstruction method provided by the present invention can achieve complete reconstruction of the frequency hopping signal.

The invention is well implemented in accordance with the above-described embodiments. It should be noted that, based on the above design principle, even if some insubstantial modifications or modifications are made on the basis of the disclosed structure, the adopted technical solution is still the same as the present invention, and therefore, the technical solution is also within the scope of the present invention.

Claims (8)

1. A method for adaptively reconstructing a translation invariant spatial compressed sample, comprising the steps of:

s1, constructing a translation invariant space compression sampling system to perform multi-channel sampling on the input time-varying signal to obtain sampling data of each channel;

s2, inputting the sampling data into a learning machine, training the sampling data by utilizing a learning mechanism, and obtaining a signal space to which the input time-varying signal belongs;

and S3, adaptively adjusting the reconstruction filter according to the obtained signal space to realize the reconstruction of the input time-varying signal.

2. The adaptive reconstruction method for the translational invariant space compressive sampling as recited in claim 1, wherein said translational invariant space compressive sampling system comprises a plurality of parallel decomposition filters having inputs receiving input time varying signals, a digital-to-analog converter having an input connected to an output of each of said decomposition filters, and an output connected to an input of a learning machine.

3. The adaptive reconstruction method for translational invariant spatial compressive sampling as claimed in claim 1, wherein in step S1, the model of the input time-varying signal is:

wherein,is a translation invariant space V_jGenerating function of C_j[n]For translation to a constant space V_jZ represents a set of integers, said input time varying signal x (t) ∈ W, where W is the signal space and the generating function of W isλ_m∈{0，1，L，r-1}。

4. The adaptive reconstruction method for translational invariant space compressive sampling according to claim 3, wherein in step S1, the compressive sampling model of the translational invariant space compressive 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 the ith channel decomposition filter of the translation invariant space compression sampling system, T_sIs the sampling period of the systemAnd L is the number of channels of the system.

5. The adaptive reconstruction method for translational invariant space compressive sampling as claimed in claim 4, wherein in said step S2, the learning mechanism utilizes an orthogonal matching tracking algorithm to obtain the signal space to which the input signal belongs in real time from the sampling data of each channel of the translational invariant space compressive sampling; the calculation process of the orthogonal matching tracking algorithm is as follows:

s201, first, obtaining a sampling matrix T (ω), where a sampling equation D (ω) is T (ω) C (ω);

s202, standardizing each column of the sampling matrix T (omega) to obtain a new matrix H (omega);

s203, searching the column which is best matched with the sampling equation D (omega) in the matrix H (omega)So thatFor the maximum value satisfied in the matrix H (omega)A column of (1);

s204, definition I₀＝{λ₀}，Then the sampling equation D (ω) is projected toAbove, the remaining residual amount is R¹D(ω)；

S205, searching the neutralization residue R in the matrix H (omega)¹Best matched column of D (omega)

S206, order I₁＝I₀U{λ₁}，The residual amount R¹D (omega) projection toThe last residual remaining is denoted as R²D(ω)；

And S207, continuously iterating according to the process.

6. The adaptive reconstruction method for translational invariant spatial compressive sampling as claimed in claim 5, wherein in step S207, when I is_k-1＝I_k-2U{λ_k-1}，When I is_k-1The number k of the elements satisfies:

or R^k-1D(ω)＝0

Then, the orthogonal matching tracking algorithm is stopped, spark (H (omega)) is the sparsity of the matrix H (omega),indicating a lower rounding.

7. The adaptive reconstruction method for the translational invariant space compressive sampling as recited in claim 6, wherein when the number of channels L of the translational invariant space compressive sampling system is smaller than the number r of signal space generating functions, the input time varying signal can be reconstructed by the compressed sampling data of the translational invariant space compressive sampling system.

8. The adaptive reconstruction method for translational invariant spatial compressive sampling as claimed in claim 7, wherein in the step S3, the Moore-Penrose inverse is adaptively adjusted in signal space to realize reconstruction of the input time-varying signal, and the specific steps are as follows:

s301, extracting the lambda-th signal from the sampling matrix T (omega)₀，λ₁，L，λ_k-1The column elements form a sub-matrix tau (omega), and the sub-matrix tau (omega) is an optimal matching matrix;

if C (omega) satisfies | | C (omega) | non-woven gas₀< spark (T (ω))/2, then the sampling equation D (ω) can be transformed as shown below:

D(ω)＝τ(ω)C_s(ω)

wherein, C_s(ω) is a vector obtained by removing zero elements from C (ω);

s302, then using Moore-Penrose inverse, the solution of the equation set of the above formula can be obtained:

C_s(ω)＝(τ(ω)^Hτ(ω))^-1τ(ω)^HD(ω)。