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Noise Reduction with Optimal Variable Span Linear Filters

In this paper, the problem of noise reduction is addressed as a linear filtering problem in a novel way by using concepts from subspace-based enhancement methods, resulting in variable span linear filters. This is done by forming the filter coefficients as linear combinations of a number of eigenvectors stemming from a joint diagonalization of the covariance matrices of the signal of interest and the noise. The resulting filters are flexible in that it is possible to trade off distortion of the desired signal for improved noise reduction. This tradeoff is controlled by the number of eigenvectors included in forming the filter. Using these concepts, a number of different filter designs are considered, like minimum distortion, Wiener, maximum SNR, and tradeoff filters. Interestingly, all these can be expressed as special cases of variable span filters. We also derive expressions for the speech distortion and noise reduction of the various filter designs. Moreover, we consider an alternative approach, wherein the filter is designed for extracting an estimate of the noise signal, which can then be extracted from the observed signals, which is referred to as the indirect approach. Simulations demonstrate the advantages and properties of the variable span filter designs, and their potential performance gain compared to widely used speech enhancement methods.