The complex cepstrum and bicepstrum: analytic performance evaluation in the presence of Gaussian noise

An analytic performance evaluation of the complex cepstrum, power cepstrum, bicepstrum, and power bicepstrum is presented 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 (SNRs). 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. Performance comparisons between bicepstrum and cepstrum methods suggest that the improved performance of the bicepstrum is a function of SNR, A( omega ), M, and N. >

[1]  Joseph C. Hassab,et al.  A probabilistic analysis of time delay extraction by the cepstrum in stationary Gaussian noise , 1976, IEEE Trans. Inf. Theory.

[2]  Athina P. Petropulu,et al.  Cumulant cepstrum of FM signals and high-resolution time delay estimation , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[3]  Athina P. Petropulu,et al.  Signal reconstruction from the phase of the bispectrum , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[4]  Jerry M. Mendel,et al.  ARMA parameter estimation using only output cumulants , 1990, IEEE Trans. Acoust. Speech Signal Process..

[5]  D. Brillinger.  An Introduction to Polyspectra , 1965 .

[6]  Chrysostomos L. Nikias,et al.  Time delay estimation in unknown Gaussian spatially correlated noise , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  Chrysostomos L. Nikias,et al.  Bicepstrum computation based on second- and third-order statistics with applications , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[8]  Donald G. Childers,et al.  Signal detection and extraction by cepstrum techniques , 1972, IEEE Trans. Inf. Theory.

[9]  J. V. Ness.  Asymptotic Normality of Bispectral Estimates , 1966 .

[10]  M.R. Raghuveer,et al.  Bispectrum estimation: A digital signal processing framework , 1987, Proceedings of the IEEE.

[11]  Chrysostomos L. Nikias,et al.  Estimation of multipath channel response in frequency selective channels , 1989, IEEE J. Sel. Areas Commun..

[12]  M. Hinich.  Testing for Gaussianity and Linearity of a Stationary Time Series. , 1982 .

[13]  G. R. Reddy,et al.  Signal delay and waveform estimation through differential cepstrum averaging , 1987, IEEE Trans. Acoust. Speech Signal Process..

[14]  Joseph F. Ossanna,et al.  The heuristics of cepstrum analysis of a stationary complex echoed Gaussian signal in stationary Gaussian noise , 1966, IEEE Trans. Inf. Theory.

[15]  Chrysostomos L. Nikias,et al.  The complex cepstrum of higher order cumulants and nonminimum phase system identification , 1988, IEEE Trans. Acoust. Speech Signal Process..

[16]  M. Rosenblatt,et al.  Asymptotic normality of cumulant spectral estimates , 1990 .

[17]  D. Stone.  Wavelet estimation , 1984, Proceedings of the IEEE.