Analysis of the frequency-domain Wiener filter with the prediction gain

This paper presents a theoretical analysis on the performance of the optimal noise-reduction filter in the frequency domain. Using the autoregressive (AR) model to model both the clean speech and noise, we build the relationship between the Wiener filter and the AR parameters of the clean speech and noise signals. We show that if noise is not predictable, the Wiener filter is mostly related to the AR parameters of the desired speech signal. On the contrary, if the desired signal is not predictable, the Wiener filter is then mostly related to the AR parameters of the noise signal. More importantly, we provide the bounds for noise reduction, speech distortion, and SNR improvement, and show that the performance of the Wiener filter in terms of SNR improvement and degree of noise reduction and speech distortion is closely related to the prediction gain of the desired speech and noise signals.