A propagation approach to modelling the joint distributions of clean and corrupted speech in the Mel-Cepstral domain

This paper presents a closed form solution relating the joint distributions of corrupted and clean speech in the short-time Fourier Transform (STFT) and Mel-Frequency Cepstral Coefficient (MFCC) domains. This makes possible a tighter integration of STFT domain speech enhancement and feature and model-compensation techniques for robust automatic speech recognition. The approach directly utilizes the conventional speech distortion model for STFT speech enhancement, allowing for low cost, single pass, causal implementations. Compared to similar uncertainty propagation approaches, it provides the full joint distribution, rather than just the posterior distribution, which provides additional model compensation possibilities. The method is exemplified by deriving an MMSE-MFCC estimator from the propagated joint distribution. It is shown that similar performance to that of STFT uncertainty propagation (STFT-UP) can be obtained on the AURORA4, while deriving the full joint distribution.