An Efficient CRT Based Algorithm for Frequency Determination from Undersampled Real Waveform

Abstract

The Chinese Remainder Theorem (CRT) based frequency estimation has been widely studied during the past two decades. It enables one to estimate frequencies by sub-Nyquist sampling rates, which reduces the cost of hardware in a sensor network. Several studies have been done on the complex waveform; however, few works studied its applications in the real waveform case. Different from the complex waveform, existing CRT methods cannot be straightforwardly applied to handle a real waveform's spectrum due to the spurious peaks. To tackle the ambiguity problem, in this paper, we propose the first polynomial-time closed-form Robust CRT (RCRT) for the single-tone real waveform, which can be considered as a special case of RCRT for arbitrary two numbers. The time complexity of the proposed algorithm is O(L), where L is the number of samplers. Furthermore, our algorithm also matches the optimal error-tolerance bound.