Accurate frequency estimation of multiple complex and real sinusoids based on iterative interpolation

Abstract

Frequency estimation of multiple complex and real sinusoids in noise has attracted wide attention in many fields. In this paper, two frequency domain parametric methods are proposed to estimate the frequencies of multiple complex and real sinusoids accurately. The first method for complex sinusoids adopts Discrete Fourier Transform (DFT) and interpolation algorithm to obtain the coarsely estimated frequencies, and then the interpolation is used iteratively to refine the estimated frequencies. In each step, the estimated frequency components are subtracted to reduce spectrum leakage. The second method for multiple real sinusoids, which is modified based on the first one, focuses on reducing the spectrum leakage caused by negative frequencies and then employs iterative interpolation to refine the estimated frequencies. Simulation results show that two proposed methods have lower mean square error (MSE) and signal-to-noise ratio (SNR) breakdown threshold than other frequency domain parametric methods, and are capable of achieving the Cramér-Rao lower bound (CRLB) for both multiple complex and real signals under a wide range of SNR.