Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT

Abstract

An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.

Keywords

• Frequency estimation
• FFT
• DTFT
• interpolation