THE COMPLEX CEPSTRUM AND BICEPSTRUM - ANALYTIC PERFORMANCE EVALUATION IN THE PRESENCE OF GAUSSIAN-NOISE

Simulation results in higher order spectrum estimation are once again dominating signal-processing studies. However, analytical studies of higher order spectra-based methods need to be developed much further before we can know how effective recently introduced methods are over existing ones. The purpose of this paper is to present an analytic performance evaluation of the complex cepstrum, power cepstrum, bicepstrum, and power bicepstrum by providing approximate expressions of the bias and variance of the cepstrum parameters due to the presence of Gaussian noise. The approximations are based on the asymptotic properties of bispectrum estimates and they are valid for moderate signal-to-noise ratios (SNR's). The assumed model consists of a deterministic signal (e.g., multiple echoes) in additive white Gaussian noise and finite length data. The validity of the analytic expressions is verified with Monte Carlo simulations, and performance comparisons between bicepstrum and cepstrum methods are presented. © 1990 IEEE