Method for collecting signal with sampling frequency lower than Nyquist frequency

摘要

A method for collecting a signal with a frequency lower than a Nyquist frequency includes, by a data transmitting end, selecting a suitable transformation base matrix for an input signal, deriving a sparse representation of the signal using the transformation base matrix to determine a sparsity of the signal, calculating a number M of compressive sampling operations according to the sparsity, sampling the signal with fNYQ/M using M channels, and integrating sampling values of each channel to obtain M measurement values. A reconstruction end reconstructs an original signal by solving optimization problems. Based on theory, compressive sampling can be performed on a sparse signal or a signal represented in a sparse manner with a frequency much lower than the Nyquist frequency, overcoming restrictions of the typical Nyquist sampling theorem. The method can be implemented simply and decrease pressure on data collection, storage, transmission and processing.

主权项

1. A method of collecting a signal with a sampling frequency lower than a Nyquist frequency, comprising:
determining, by a data transmitting end, a sparsity k of an original input signal x, calculating a number M of compressive sampling operations according to the sparsity k, sampling the original input signal x with a frequency fNYQ/M using M channels respectively, wherein fNYQ is the Nyquist frequency of the original input signal x, integrating sampling values of each channel to obtain M measurement values y, and then transmitting the M measurement values y to a data receiving end; and restoring, by the data receiving end, the received M measurement values y to a sparse representation of the original input signal x using an orthogonal matching pursuit algorithm, and then obtaining the original input signal x by performing an inverse transformation on the sparse representation.