Reconstruction of Sub-Nyquist Random Sampling for Sparse and Multi-Band Signals

TL;DR

This paper introduces new random sampling recovery algorithms for sparse and multi-band signals that operate at sub-Nyquist rates without requiring prior knowledge of signal sparsity, supported by theoretical conditions and extensive simulations.

Contribution

It proposes novel sub-Nyquist random sampling recovery algorithms that do not need anti-aliasing filters or prior sparsity information, with proven convergence conditions.

Findings

Algorithms successfully recover sparse signals at sub-Nyquist rates.

Theoretical conditions ensure convergence of the proposed methods.

Simulation results confirm the effectiveness of the algorithms.

Abstract

As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling rates. Hence, lower sampling rates (i.e., sub-Nyquist) are considered to be cost efficient. A well-known approach is to consider sparse signals that have fewer nonzero frequency components compared to the highest frequency component. For the prior knowledge of the sparse positions, well-established methods already exist. However, there are applications where such information is not available. For such cases, a number of approaches have recently been proposed. In this paper, we propose several random sampling recovery algorithms which do not require any anti-aliasing filter. Moreover, we offer certain conditions under which these recovery techniques converge to the signal. Finally, we also confirm the performance of the above methods through extensive simulations.