An Analysis of Adaptive Recursive Smoothing with Applications to Noise PSD Estimation

Abstract

First-order recursive smoothing filters using a fixed smoothing constant are in general unbiased estimators of the mean of a random process. Due to their efficiency in terms of memory consumption and computational complexity, they are of high practical relevance and are also often used to track the first-order moment of nonstationary random processes. However, in single-channel speech-enhancement applications, e.g., for the estimation of the noise power spectral density, an adaptively changing smoothing factor is often employed. Here, the adaptivity is used to avoid speech leakage by raising the smoothing factor when speech is likely to be present. In this paper, we investigate the properties of adaptive first-order recursive smoothing factors applied to noise power spectral density estimators. We show that in contrast to a smoothing with fixed smoothing factors, adaptive smoothing is in general biased. We propose different methods to quantify and to compensate for the bias. We demonstrate that the proposed correction methods reduce the estimation error and increases the perceptual evaluation of speech quality scores in a speech enhancement framework.