CN101409558A - Analog-digital converter base on compression sampling technique - Google Patents

Abstract

The invention aims at providing an ADC based on compressing and sampling technique which does not consider the sampling frequency, is only related to the openness of a signal, can collect compressed format data directly, and can greatly reduce the data collection quantity. The ADC consists of an analog signal, a compressing and sampling ADC and a compressed format binary digital signal. The analog signal is connected with the compressing and sampling ADC which is connected with the compressed format binary digital signal. The ADC can realize the function of compressing data while converting the analog signal to the digital signal, namely, the compressed format digital signal is collected from the analog signal directly, and the data collection quantity is greatly reduced compared with the traditional ADC.

Description

Analog to digital converter based on the compression sampling technology

(1) technical field

The present invention relates to digital technology, just be based on the analog to digital converter of compression sampling technology specifically.

(2) background technology

Data compression is exactly the redundancy section that removes in the data, and traditional data compression coding theory can be divided into lossless compression algorithm and lossy compression method algorithm two classes usually based on information theory.Lossless compression algorithm does not have loss exactly in the data compression and decompression process.The lossy compression method algorithm can cause the loss of some comentropies, is acceptable as long as this loss is limited within the allowed band still.Classical compaction coding method has three types usually: predictive coding, transition coding, statistical coding.Newer in addition have fractal image, a wavelet image compressed encoding etc.

2006, professor Candes of California Inst Tech USA proposed a kind of new data compression algorithm " compression sampling (Compressive Sampling, CS) ", and this method is mainly used in the compression of view data at present.The compression sampling technology is different with traditional data compression, and traditional data compression algorithm is to collect complete data earlier, and then data are compressed processing; Compression sampling then is the data that directly obtain compressed format, compares obvious tool with traditional data compression and has an enormous advantage.

The compression sampling technology can with traditional ADC combination, be made into new compression sampling ADC, realize directly collecting the data of compressed format.Traditional ADC is carrying out need satisfying sampling thheorem analog-to-digital the time, just sample frequency must greater than highest frequency in the signal more than 2 times the time, the digital signal after the sampling could intactly keep the information in the primary signal.If signal frequency is higher, the data volume that obtains of sampling so also is huge.Adopt the ADC of compression sampling technology then not need to consider sample frequency, only relevant with the sparse property of signal, if signal itself is sparse or certain orthogonal transform of process is sparse afterwards, so just can directly gather the data of compressed format, significantly reduce the collection capacity of data.

(3), summary of the invention

The object of the present invention is to provide a kind of do not need to consider sample frequency, only relevant with the sparse property of signal, can directly gather data of compressed format, significantly reduce the analog to digital converter based on the compression sampling technology of data acquisition amount.

The object of the present invention is achieved like this: it is made up of the binary digital signal of analog signal, compression sampling ADC and compressed format.Analog signal connects compression sampling ADC, and compression sampling ADC connects the signal of the binary system composition of compressed format.

The present invention is based on the analog to digital converter of compression sampling technology, also have following technical characterictic:

Described compression sampling ADC comprises microcontroller 1, traditional digital to analog converter DAC 2, analog multiplier 3, integrating circuit 4 and traditional ADC 5.Microcontroller 1 connects traditional digital to analog converter DAC 2, and traditional digital to analog converter DAC 2 connects analog multiplier 3, and analog multiplier 3 connects integrating circuit 4, and integrating circuit 4 connects traditional ADC 5.

The present invention is based on the analog to digital converter of compression sampling technology, the course of work is as follows: at first sending instruction by microcontroller 1, will to be stored in m group length on the microcontroller 1 in advance be that the obedience average of n is zero, variance is the random number of the normal distribution of 1/m, and the input that will disperse by traditional digital to analog converter DAC 2 converts analog signal φ to _j(t), j=1 ..., m, analog signal x of input (t) and φ _j(t), j=1 ..., m multiplies each other by analog multiplier 3, obtains new analog signal x (t) * φ _j(t), then new analog signal is carried out integration by integrating circuit 4, adopt 5 pairs of integrations of traditional ADC analog signal sampling afterwards to handle again, the binary number y (j) that promptly can obtain dispersing after handling, j=1 ..., m.

The present invention is the function that can realize data compression when analog signal conversion is digital signal, just directly collects the digital signal of compressed format and traditional ADC and relatively can significantly reduce the data acquisition amount from analog signal.

(4) description of drawings

Fig. 1 is a compression sampling ADC overall block-diagram of the present invention;

Fig. 2 is the circuit diagram of compression sampling ADC of the present invention.

(5), embodiment

The invention will be further described for example below in conjunction with accompanying drawing.

Embodiment 1, and in conjunction with Fig. 2, traditional digital to analog converter DAC of the present invention (2), analog multiplier (3), integrating circuit (4) and traditional ADC (5) can utilize ready-made module and product at present, and their model is not had specific (special) requirements.For microcontroller (1), has the function of storage data; Need write corresponding program, make it can satisfy the function of compression sampling.At first adopting C language compilation program to produce the m group length is that the obedience average of n is that zero variance is the random number of the normal distribution of 1/m, and is converted into binary number, adopts assembler language that two system numbers are write and are kept in the microprocessor then.Write control program then, make microcontroller can send instruction, the binary system random number of importing is converted into analog signal φ by traditional digital to analog converter DAC (2) _j(t), j=1 ..., m, establishing compression sampling ADC need be discrete signal with the analog signal conversion that collects every time Δ T, then controller (1) sends once command every time Δ T.

The effect of tradition digital to analog converter DAC (2) is after receiving the discrete random number of being exported by microcontroller (1), converts thereof into to be analog signal, by circuit analog signal is input to analog multiplier (3) again.Analog multiplier (3) then is to realize analog signal x (t) that will collect and the analog signal φ that is come by traditional digital to analog converter DAC (2) conversion _j(t), j=1 ..., m carries out multiplying, and is faster for arithmetic speed, adopts parallel structure, promptly adopts m analog multiplier to seize the opportunity computing simultaneously.The analog signal of analog multiplier (3) output is input to integrating circuit (4) lining, adopts m integrating circuit equally, finish integral operation fast.Analog signal to integrating circuit (4) output adopts m traditional ADC (5) to carry out analog-to-digital conversion respectively then, obtains the dateout y (j) of binary format, j=1 ..., m has so just realized the repertoire of compression sampling ADC.

The present invention is applicable to the analog signal that has sparse characteristic or have approximate sparse characteristic, and for analog signal, so-called sparse property is meant that signal launches under some orthogonal basis after, the n that an obtains coefficient comprises non-zero points s, satisfy s＜＜n; Be similar to sparse property and be meant, after under some orthogonal basis, launching, s in the n that the obtains coefficient (s＜＜n) individual coefficient is relatively large, and wherein n-s coefficient then approaches zero.It is s that the signal that satisfies above-mentioned sparse property is referred to as degree of rarefication.Because analog signal x (t) can regard limited discrete factor alpha as _iWith continuous orthogonal basis ψ _iThe form of the sum of products (t)

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\ψ}}_i\left(t\right)$

If factor alpha _iBe comprise s＜＜a n non-zero points, can claim that then analog signal x (t) is sparse.α in the formula _iBe signal decomposition coefficient, α _i=＜x, ψ _iOr α=ψ ^TX; ψ _iBe n * 1 orthogonal basis column vector.Wherein orthogonal basis ψ's can have multiple choices, used sine wave during such as Fourier transform, the various wavelet basiss of wavelet transformation etc.

The compression sampling of analog signal is adopted the mode of Linear Mapping

y＝Φψα＝Θα

The ψ matrix is n continuous basic function ψ in the formula _i(t), i=1 ..., n; The Φ matrix then is m continuous function φ at random _j(t), j=1 ..., m.Factor alpha=[α then ₁..., α _n] can be reconstructed by finding the solution following optimization problem:

(P1) $\widehat{\mathrm{\α}}=\min {\left|\right|\widetilde{\mathrm{\α}}\left|\right|}_1$ And $\mathrm{\Θ}\widetilde{\mathrm{\α}}=y$

The signal y (j) that measures, j=1 ..., m is:

$y\left(j\right)=\underset{-\∞}{\overset{+\∞}{\∫}}x\left(\mathrm{\τ}\right){\mathrm{\φ}}_j\left(\mathrm{\τ}\right)\mathrm{d\τ}$

$y\left(j\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i\underset{-\∞}{\overset{+\∞}{\∫}}{\mathrm{\ψ}}_i\left(\mathrm{\τ}\right){\mathrm{\φ}}_j\left(\mathrm{\τ}\right)\mathrm{d\τ}$

φ _j(t), j=1 ..., m, φ _j(t) for also being continuous function.Θ entry of a matrix element can calculate according to following formula, that is:

${\mathrm{\θ}}_{j,i}=\underset{-\∞}{\overset{+\∞}{\∫}}{\mathrm{\ψ}}_i\left(\mathrm{\τ}\right){\mathrm{\φ}}_j\left(\mathrm{\τ}\right)\mathrm{d\τ}$

J=1 ..., m, i=1 ..., n promptly constitutes matrix m * n dimension matrix Θ.

For test data the situation of noise effect is arranged, then

y＝Θα+e

E is for measuring noise in the formula.The reconstruct problem of compression sampling then becomes following (P2) problem

(P2)

And ${\left|\right|\mathrm{\Θ}\widetilde{\mathrm{\α}}-y\left|\right|}_2\≤\mathrm{\ϵ}$

ε satisfies ‖ e ‖ for measuring the upper energy limit of noise e in the formula ₂≤ ε.(P2) optimized Algorithm that just adopts of problem is different.According to the principle of compression sampling, in the time of m 〉=3s (P1) and (P2) optimization problem have unique exact solution.

Find the solution (P1) and (P2) can adopt the method for linear programming, find the solution by the Matlab programming, the method for linear programming commonly used has interior point method and simplex method, finds the solution and obtains factor alpha=[α ₁..., α _n] unique exact solution Afterwards, can find the solution by following formula and obtain analog signal x (t):

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\ψ}}_i\left(t\right)$

By sampling thheorem x (t) is carried out discretization and handle, just can obtain x (i), i=1 ..., n.

The compression sampling analog to digital converter mainly is the data y (j) that collects compressed format, j=1 ..., m, for the reconstruct of signal, can finish by the Matlab coding, only need the run signal reconfiguration program in client, both can obtain signal x (i), i=1 ..., n.

The value of measure dot number m is relevant with the degree of rarefication of signal, and establishing the signal degree of rarefication is s, and then m 〉=3s, so signal is sparse more, under the situation of same reconstructed error, can adopt few more measure dot number m.

The present invention is applicable to have sparse property or the sparse signal of approximation, from the angle of frequency content, is that the signal of narrow-band characteristic is suitable for for frequency content.The bridge structure that relates in the civil engineering works structure health monitoring for example, the structural vibration response signal of multilayer, skyscraper all has the frequency content narrow-band characteristic, so the present invention can be suitable for this type of signal.The signal that has the high-frequency narrow-band characteristic in addition for frequency content, the present invention is suitable for, because high-frequency signal needs very high sample frequency, traditional ADC need sample and obtain mass data, and the saving data acquisition amount that the present invention can be a large amount of.

The present invention is carried out numerical simulation, and the result shows that the present invention compares with traditional ADC, Can save about data acquisition amount 40%-60%.

Claims (3)

1. analog to digital converter based on the compression sampling technology, it is made up of the binary digital signal of analog signal, compression sampling ADC and compressed format; It is characterized in that: analog signal connects compression sampling ADC, and compression sampling ADC connects the binary digital signal of compressed format.

2. a kind of analog to digital converter based on the compression sampling technology according to claim 1, described compression sampling ADC comprise microcontroller (1), traditional digital to analog converter DAC (2), analog multiplier (3), integrating circuit (4) and traditional ADC (5); It is characterized in that: microcontroller (1) connects traditional digital to analog converter DAC (2), and traditional digital to analog converter DAC (2) connects analog multiplier (3), and analog multiplier (3) connects integrating circuit (4), and integrating circuit (4) connects traditional ADC (5).

3. analog to digital converter based on the compression sampling technology, the course of work is as follows: at first sending instruction by microcontroller (1), will to be stored in m group length on the microcontroller (1) in advance be that the obedience average of n is that zero variance is the random number of the normal distribution of 1/m, and the input that will disperse by traditional digital to analog converter DAC (2) converts analog signal φ to _j(t), j=1 ..., m, the analog signal x of input (t) are respectively and φ _j(t), j=1 ..., m multiplies each other by analog multiplier (3), obtains new analog signal x (t) * φ _j(t), then new analog signal is carried out integration by integrating circuit (4), adopt traditional ADC (5) that the analog signal sampling after the integration is handled again, the binary number y (j) that promptly can obtain dispersing after handling, j=1 ..., m.

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