Signal reconstruction technical scheme for sampling with rate lower than Nyquist rate

Abstract

The invention relates to a signal reconstruction technical scheme for sampling with rate lower than nyquist rate. The signal reconstruction scheme comprises the following steps of: firstly, solving a transformation basic matrix (signals x to be reconstructed thereon are sparse on the transformation basic matrix), modulating the transformation basic matrix with a cutting sequence, filtering by means of a digital filter, sampling the filtered signals, then generating compressive sensing arithmetic operators, and finally obtaining reconstructed signals by solving an optimized problem through the sparse inverse transformation. The invention aims to provide the signal reconstruction technical scheme for sampling with rate lower than the Nyquist rate, satisfy the needs for people in solving the contradictions between the increasingly widening signal bandwidth as well as the increasingly quickening sampling frequency and the requirements for reducing processing time and various costs reduce the signal sampling frequency and data transmission and storage cost, further remarkably shorten the signal processing time and reduce the computational expense, and accurately reconstruct signals.

Description

technical field [0001] The invention relates to a technical method for signal reconstruction, which belongs to the field of signal acquisition and reconstruction. Background technique [0002] Nyquist sampling theorem is an important theoretical basis to guide how to sample. It states that the sampling rate must be more than twice the highest frequency of the signal to accurately reconstruct the signal. For wideband signals, sampling at the Nyquist rate will put enormous pressure on signal acquisition, storage, and processing, and the Nyquist sampling theorem does not take advantage of the sparsity of such signals. The theory of Compressive Sensing (CS) points out that as long as the signal is compressible or sparse in a certain transform domain, then an observation matrix unrelated to the transform base can be used to project the transformed high-dimensional signal to a low dimensional space, and then by solving an optimization problem, the original signal can be reconstr...

AI Technical Summary

Problems solved by technology

For wideband signals, sampling at the Nyquist rate will put enormous pressure on signal acquisition, storage, and processing, and the Nyquist sampling theorem does not take advantage of the sparsity of such signals

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