High-precision frequency estimator by using discrete Fourier transform and asymmetric discrete time Fourier transform samples

Abstract

Fast and accurate frequency estimation is significant for instrumentation and measurement. A sinusoid frequency estimator using discrete Fourier transform (DFT) is presented. DFT is implemented on the sinusoid and the maximum DFT bin is sought out to obtain the coarse estimate. Different from all the existing methods, two asymmetric discrete-time Fourier transform (DTFT) samples situated at arbitrary positions on the same side of the maximum DFT bin are employed to get the fine estimate. The theoretical mean square error is analyzed. To evaluate the estimation performance, the presented estimator is compared with the Cramer–Rao lower bound (CRLB) and state-of-art estimators through computer simulations. Simulation results demonstrate that the presented algorithm is closer to the CRLB compared with the competing methods when the signal-to-noise ratio (SNR) varies in a large range and is unbiased at high SNR.