Abstract
Abstract In this paper, we provide an overview of some recently introduced principles and ideas for speech enhancement with linear filtering and explore how these are related and how they can be used in various applications. This is done in a general framework where the speech enhancement problem is stated as a signal vector estimation problem, i.e., with a filter matrix, where the estimate is obtained by means of a matrix-vector product of the filter matrix and the noisy signal vector. In this framework, minimum distortion, minimum variance distortionless response (MVDR), tradeoff, maximum signal-to-noise ratio (SNR), and Wiener filters are derived from the conventional speech enhancement approach and the recently introduced orthogonal decomposition approach. For each of the filters, we derive their properties in terms of output SNR and speech distortion. We then demonstrate how the ideas can be applied to single- and multichannel noise reduction in both the time and frequency domains as well as binaural noise reduction.
Highlights
The problem of speech enhancement, or noise reduction as it is sometimes called, is a well-known, longstanding problem with important applications in, for example, speech communication systems and hearing aids, where additive noise can, and often does, have a detrimental impact on the speech quality
The speech enhancement problem is stated as the problem of finding a rectangular filter matrix for estimating the speech signal vector from a noisy signal observation vector
Another way to measure the distortion of the desired signal vector due to the filtering operation is via the speech distortion index defined as: E xfd − xQ H xfd − xQ
Summary
1.1 Introduction The problem of speech enhancement, or noise reduction as it is sometimes called, is a well-known, longstanding problem with important applications in, for example, speech communication systems and hearing aids, where additive noise can, and often does, have a detrimental impact on the speech quality. We proceed to present an alternative approach based on the orthogonal decomposition, and we use this to derive optimal filters These are compared in terms of their noise reduction and speech distortion properties. The objective of speech enhancement (or noise reduction) is to estimate xQ from y This should be done in such a way that the noise is reduced as much as possible with no or little distortion of the desired signal vector [1,13,14,15]. In the rest of this study, we consider two important cases: without (conventional approach) and with the orthogonal decomposition of the speech signal vector
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