Sampling Analysis Of Compressed Sensing Based Analog To Information Converter

Nyquist sampling theory is the most widely used theory to sample signal, but the theory has clear request to sampling rate, which is the sampling rate must be above two times of the frequency of the sampled signal, then the spectrum aliasing which can cause some information of the signal missing can be avoid. And realize accurate reconstruction to the original signal. But nowadays with the rapid development of science and technology, some sampled signals’ frequency is growing higher and higher. Therefore it is a serious problem to the sampling rate of ADC(Analog to Digital Converter). And compressed sensing is a new sampling theory which adopts the new algorithm. It can solve the high sampling rate problem which Nyquist sampling theory brings.Compared to the traditional Nyquist sampling theory, compressed sensing has the advantages of low sampling frequency without losing the precision, which breaks the limit of that Nyquist sampling theory requires sampling rate must be above two times of the sampled signal’s frequency. This paper focuses on compressed sensing theory’s analysis. The theoretical frame and sampling conditions is analyzed firstly. The sampled signal must be sparse, which can be achieved through sparse transformation base. And transform the signal with observation matrix which satisfies the Restricted Isometry Property(RIP). Then sample and reconstruct the signal. Compressed sensing is applied in the process of sampling analog signal with harmonics, the sampling system is Analog-to-Information Converter(AIC). Simulate and analyze the AIC system through Matlab, and construct a pseudo-random sequence, mixing link, integral and AD sampling, and build the equivalent matrix according to the role of each link,then sample the sinusoidal signal containing multiple harmonics with the frequency which below two times of the frequency of the sampled signal. Use Orthogonal Matching Pursuit(OMP) reconstructs the original signal. Research each link’s noise,including Gaussian white noise introduced in input signal, quantization noise and the noise introduced by device in the practical application. Analysis these noises’ influence to the reconstructed signal’s SNR and reconstruction error through changing parameters. Finally, use actual device to propose a way to construct each link of AIC.