Frequency Estimation of Multiple Sinusoids with Three Sub-Nyquist Channels

TL;DR

This paper proposes a method for accurately estimating multiple sinusoid frequencies using only three sub-Nyquist channels with pairwise coprime undersampling ratios, enabling unique frequency determination.

Contribution

It demonstrates that three sub-Nyquist channels with coprime ratios suffice for unique frequency estimation, extending prior work limited to fewer channels or higher sampling rates.

Findings

Three coprime sub-Nyquist channels enable unique frequency estimation.

Two channels may fail to resolve frequency ambiguities under certain conditions.

Numerical experiments confirm the theoretical analysis and effectiveness.

Abstract

Frequency estimation of multiple sinusoids is significant in both theory and application. In some application scenarios, only sub-Nyquist samples are available to estimate the frequencies. A conventional approach is to sample the signals at several lower rates. In this paper, we address frequency estimation of the signals in the time domain through undersampled data. We analyze the impact of undersampling and demonstrate that three sub-Nyquist channels are generally enough to estimate the frequencies provided the undersampling ratios are pairwise coprime. We deduce the condition that leads to the failure of resolving frequency ambiguity when two coprime undersampling channels are utilized. When three-channel sub-Nyquist samples are used jointly, the frequencies can be determined uniquely and the correct frequencies are estimated. Numerical experiments verify the correctness of our analysis and conclusion.