Frequency Estimator Based on Spectrum Correction and Remainder Sifting for Undersampled Real-Valued Waveforms

Abstract

Frequency estimation of undersampled waveforms receives increasing attention in communication, radar signal processing, instrumentation and measurements, and so on. However, due to the lack of recognizing the correct remainder between two side spectra, the existing Chinese Remainder Theorem (CRT)-based frequency estimators can hardly deal with real-valued signals. To achieve this goal, this paper proposes an estimator combining spectrum correction (aiming to enhance reconstruction accuracy by incorporating the fractional parts of DFT remainders), closed-form CRT, and a remainder sifting approach. Based on the detection of an undersampled waveform's zero crossing point, this solution can pick out the correct remainder between two side spectra, which ensures that the CRT achieves a valid reconstruction. Compared with the existing Maroosi-Bizaki estimator, the proposed method not only enlarges the upper bound of frequency recovery but also possesses higher reconstruction accuracy (the relative error is less than 0.002%) with lower consumption of computational complexity. The numerical results verify the superior performances of our estimator.

Digital instantaneous frequency measurement with wide bandwidth for real-valued waveforms using multiple sub-Nyquist channels

“…Suitable parameter settings can reduce the measurement error and enhance the noise resistance. Numerical experiments have verified that our proposed algorithm has better noise immunity and adaptability to high-dynamic signals in a narrow time window than [25]. Since we only need a short analysis time window, our work can also be extended to chirp signal parameter estimation [26,27].…”

“…Specifically, assuming the three sampling rates are 3 Hz, 5 Hz and 7 Hz, the bandwidth based on [22,23] is 0-11 Hz compared with 0-105 Hz based on our method. Huang used phase spectrum analysis to select the correct folded frequencies [25], requiring the real-valued signal first pass through a zero-crossing detector. However, their DFT-based method cannot provide a narrow enough frequency resolution for high-dynamic signals.…”

Digital Instantaneous Frequency Measurement of a Real Sinusoid Based on Three Sub-Nyquist Sampling Channels

“…In the real signal case, the value of b k must be estimated in advance. In [29], a method to estimate b k by employing a triggering circuit to detect the waveform's zero crossing point 'O' is proposed.…”

A new frequency estimation method for a real-valued waveform with multiple sub-Nyquist channels based on the ESPRIT algorithm

“…Therefore, the CRT is mostly applicable only in the frequency estimation for complex signals. To measure the frequency of the real-valued signal, Huang [8] added a zero-crossing detector in front of the sampling channel and selected the right remainder according to the signal phase. But this method has a limited noise immunity considering that the signal phase is easily affected by noise.…”