High sampling rate or high resolution in a sub-Nyquist sampling system

Abstract

A digital signal acquisition system consists of two steps: sampling and quantization. Sampling maps a continuous signal to a digital signal, which then is quantized into a finite number of bits. Generally, a high sampling rate can ensure robustness to noise, while high resolution means less distortion. However, an analog-to-digital converter (ADC) cannot provide a high sampling rate and high resolution simultaneously. The bit rate is constrained, and there is a tradeoff between sampling rate and resolution. In this paper, we investigate the signal reconstruction in the framework of a compressed sensing based sub-Nyquist sampling system. We also study the noise introduced in the sampling stage and the quantization stage and evaluate the recovered signal-to-noise ratio (RSNR) with respect to the sampling rate and resolution. Considering potential application, we study the tradeoff involved in choosing the sampling rate and number of quantization bits according to the input SNR. Finally, we derive a relationship between RSNR and signal sparsity order, sampling rate, and number of quantization bits.