Shockwave Signal Downsampling Rate Acquisition Based on Sparse Fourier Transform

Abstract

The wireless distributed transient shockwave testing system based on Nyquist sampling needs to keep high sampling rate and front-end data processing rate, which leads to the shortening of the life cycle of wireless nodes. In order to solve the above problems, the shockwave signal acquisition technology based on Sparse Fourier Transform is proposed in this paper. The specific method is to use the sparse characteristics of the frequency domain of the transient shockwave signal to collect the frequency domain by downsampling, reduce the amount of acquired data. The simulation results of the above experiments are compared with the simulation results of Compressed Sensing low sampling observation. The experimental results show that the time-domain acquisition accuracy error of the proposed framework is less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> when the Nyquist sampling rate is less than 8 times, and the mean relative error in time domain is only 0.01%. And compared with the acquisition framework based on Compressed Sensing theory, the reconstructed mean absolute error of the proposed method is reduced by 88.66% in the case of the same downsampling multiple. Moreover, this method does not need to store the high-dimensional random observation matrix similar to Compressed Sensing, which overcomes the defect of hardware implementation difficulty.