Frequency Estimation of Multiple Components using Chinese Remainder Theorem

Abstract

Frequency estimation is a very important step to correctly detect a signal components. Nowadays, frequency estimation is required in many applications such biomedical signals, spectrum sensing, and military systems. However, as most of these applications require wide bands signals, the implementation of conventional sampling schemes at the Nyquist rate becomes very challenging. Hence, it is primordial to propose advanced frequency estimation methods at sub-Nyquist sampling rates. In literature, Chinese remainder theorem (CRT) has been proposed to estimate the components of a single frequency signal. However, its extension to multiple components has not been addressed due to the complexity of the estimation algorithm. In this paper, we extend the CRT further by proposing a new approach for frequency estimation of a signal with multiple components as long as they have a particular pattern. The results have been validated by Monte-Carlo simulations and compared with the well-known MUSIC algorithm.