Chinese remainder theorem-based frequency estimation for undersampled signals without multi-rate sampling

Abstract

Frequency estimation of undersampled waveforms has received considerable attention in communications, instrumentation, and measurement fields. Chinese remainder theorem (CRT)-based reconstruction is a prevalent frequency estimation method. However, the existing CRT-based methods heavily rely on multi-rate sampling and face challenges in handling real-valued undersampled waveforms and multi-frequency scenarios due to inherent ambiguities. To overcome these limitations, we propose a novel CRT-based frequency estimation method that generates aliasing information through the phase change caused by delay and estimates frequencies by solving the congruence equations constructed using the aliasing findings. The proposed method requires only a specially designed periodic nonuniform sampling of order 2, which avoids multi-rate sampling and has a simpler hardware implementation. Owing to the clear correspondence between the multiple frequencies and their aliasing frequencies, the proposed method can be applied to multi-frequency estimations. Furthermore, the proposed method is extended to real-valued waveforms by incorporating grouping operations and frequency estimation sifting. In summary, this study overcomes the main limitations of CRT in frequency estimation of undersampled waveforms and shows superior applicability to real-valued signals and multi-frequency cases, which may lead to a renaissance of CRT in undersampling signal processing.