A highly accurate DFT-based parameter estimator for complex exponentials

Abstract

A highly accurate DFT-based complex exponential parameter estimation algorithm is presented in this paper. It will be shown that for large number of samples and high signal to noise ratio (SNR), the phase estimation error variance performance is only 0.0475 dB above the Cramer-Rao lower bound (CRLB) for phase estimation with unknown frequency and phase. The amplitude estimation error variance performance was found to lay on the CRLB for amplitude estimation. Exact phase and amplitude estimation can be achieved in the noiseless case with this algorithm. The algorithm has low implementation computational complexity and is suitable for numerous real time digital signal processing applications.