Statistical analysis of the autoregressive modeling of reverberant speech

Hands-free speech input is required in many modern telecommunication applications that employ autoregressive (AR) techniques such as linear predictive coding. When the hands-free input is obtained in enclosed reverberant spaces such as typical office rooms, the speech signal is distorted by the room transfer function. This paper utilizes theoretical results from statistical room acoustics to analyze the AR modeling of speech under these reverberant conditions. Three cases are considered: (i) AR coefficients calculated from a single observation; (ii) AR coefficients calculated jointly from an M-channel observation (M > 1); and (iii) AR coefficients calculated from the output of a delay-and sum beamformer. The statistical analysis, with supporting simulations, shows that the spatial expectation of the AR coefficients for cases (i) and (ii) are approximately equal to those from the original speech, while for case (iii) there is a discrepancy due to spatial correlation between the microphones which can be significant. It is subsequently demonstrated that at each individual source-microphone position (without spatial expectation), the M-channel AR coefficients from case (ii) provide the best approximation to the clean speech coefficients when microphones are closely spaced (<0.3m).