Signal collecting method with sampling frequency lower than Nyquist frequency

Abstract

The invention discloses a signal collecting method with a sampling frequency lower than the Nyquist frequency. Firstly, an appropriate conversion basis matrix is selected for an input signal, sparsity expression is performed on the signal with the conversion basis matrix so as to determine the sparsity k of the signal, the sampling times M of compressive sampling are calculated with the sparsity, M channels are divided for respectively performing sampling on the signal in a fNTQ / M mode, integration is performed on the sampling value of each channel so as to obtain M measured values, and a reconstruction end reconstructs an original signal by solving the optimization problem. According to the signal collecting method with the sampling frequency lower than the Nyquist frequency, the compressed sensing principle serves as a basis so as to perform compressive sampling on sparse signals or signals capable of being expressed in a sparse mode with the frequency far lower than the Nyquist frequency, and limitation on the sampling frequency by the classic Nyquist sampling theorem is broken. Meanwhile, the signal collecting method with the sampling frequency lower than the Nyquist frequency is easy to carry out and reduces pressure in collecting, storing, transmitting and processing data.

Description

technical field [0001] The invention relates to a signal acquisition method with a sampling frequency lower than the Nyquist frequency, capable of compressing and sampling sparse signals or sparsely representable signals at a sampling frequency much lower than the Nyquist frequency, and reconstructing out the original signal. Background technique [0002] The Nyquist sampling theorem is the basis of modern communication and signal processing. This theorem points out that in the process of analog / digital signal conversion, when the sampling frequency is greater than or equal to twice the highest frequency of the signal, the digital signal after sampling completely retains the original signal. Information, in general practical applications, the sampling frequency is guaranteed to be 5 to 10 times the highest frequency of the signal. [0003] For broadband signals, due to their relatively high frequency, if the Nyquist sampling theorem is used to directly sample the signal, th...

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Problems solved by technology

[0003] For broadband signals, due to their relatively high frequency, if the Nyquist sampling theorem is used to directly sample the signal, the sampling frequency required is very high. The highest frequency of the existing analog-to-digital conversion devices is 1GHz, so it is difficult to meet high frequency requirements. requirements

In addition, after the signal passes through the analog-to-digital converter, it is generally stored first, and then data communication and processing are carried out. High-speed sampling requires high storage speed of the memory and processing speed of the digital signal processor, so the broadband signal is processed using the Nyquist sampling theorem. Sampling will bring enormous pressure to the acquisition, storage, transmission and processing of broadband signals

[0004] In addition, because the Nyquist sampling theorem only develops and utilizes the least prior information of the sampled signal, that is, the bandwidth of the signal, it does not take advantage of some structural characteristics of the signal itself, such as redundancy, etc.

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