Harmonics to the Rescue: Why Voiced Speech is Not a Wss Process

TL;DR

This paper argues that voiced speech is better modeled as a cyclostationary process rather than a wide-sense stationary process, leading to improved spectral estimation and source separation in speech processing.

Contribution

It introduces the use of cyclostationary modeling for voiced speech, challenging the traditional WSS assumption and demonstrating its advantages through simulations and real data.

Findings

Cyclostationary model improves spectral density estimation.

Enhanced source separation and beamforming performance.

Validation with real speech data supports the model's effectiveness.

Abstract

Speech processing algorithms often rely on statistical knowledge of the underlying process. Despite many years of research, however, the debate on the most appropriate statistical model for speech still continues. Speech is commonly modeled as a wide-sense stationary (WSS) process. However, the use of the WSS model for spectrally correlated processes is fundamentally wrong, as WSS implies spectral uncorrelation. In this paper, we demonstrate that voiced speech can be more accurately represented as a cyclostationary (CS) process. By employing the CS rather than the WSS model for processes that are inherently correlated across frequency, it is possible to improve the estimation of cross-power spectral densities (PSDs), source separation, and beamforming. We illustrate how the correlation between harmonic frequencies of CS processes can enhance system identification, and validate our findings using both simulated and real speech data.