Efficient Frequency Estimation Algorithm Based on Chirp-Z Transform

Abstract

The Discrete Fourier Transform (DFT), which can be calculated efficiently by the Fast Fourier Transform (FFT), is one of the most commonly used tools for frequency estimation of a multi-frequency exponential signal. However, the performance of the FFT is inherently affected by spectral leakage when non-coherent sampling occurs. The Chirp-Z Transform (CZT), which can refine the spectrum to the narrowband range of the source signal accurately, can be generalized to a special form of DFT. This paper proposes a CZT based algorithm which can estimate frequencies of the multi-frequency exponential signal accurately. In our method, the CZT bin, as a nonlinear equation, is firstly used to describe the correspondence among the frequencies, amplitudes, phases and the observed spectrum. Then, the above nonlinear equation is rewritten as a linear equation with unknown frequencies. We further extend the proposed method to the Discrete-time Fourier Transform (DTFT), zero-padding FFT and DFT, which are the special cases of the CZT. We also give the derivation procedure of theoretical variance of our method. In our method, the spectrum leakage is fully considered as useful information to establish the linear equation set. Therefore, it can estimate the frequencies of multi-frequency exponential signal with high accuracy. Simulation results verify the performance of the proposed method.