In this paper we derive the signal power bias that arises when spectral amplitudes are smoothed by reducing their variance in the cepstral domain (often referred to as cepstral smoothing) and develop a power bias compensation method. We show that if χ-distributed spectral amplitudes are smoothed in the cepstral domain, the resulting smoothed spectral amplitudes are also approximately χ-distributed but with more degrees of freedom and less signal power. The key finding for the proposed power bias compensation method is that the degrees of freedom of χ-distributed spectral amplitudes are directly related to their average cepstral variance. Furthermore, this work gives new insights into the statistics of the cepstral coefficients derived from χ-distributed spectral amplitudes using tapered spectral analysis windows. We derive explicit expressions for the variance and covariance of correlated χ-distributed spectral amplitudes and the resulting cepstral coefficients, parameterized by the degrees of freedom. The results in this work allow for a cepstral smoothing of spectral quantities without affecting their signal power. As we assume the parameterized χ-distribution for the spectral amplitudes, the results hold for Gaussian, super-Gaussian, and sub-Gaussian distributed complex spectral coefficients. The proposed bias compensation method is computationally inexpensive and shown to work very well for white and colored signals, as well as for rectangular and tapered spectral analysis windows.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

The following notice applies to all IEEE publications:
© IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

[Download]