Structured subspace and rank reduction techniques for signal enhancement in speech processing applications

Subspace based methods used in spectral estimation and direction finding for array signal processing persist as a topic of great interest in digital signal processing. Their increased interest over the last two decades is due in part to the proliferation of techniques which can be used to model and estimate various time and frequency domain, deterministic and statistical parameters of a signal. The numerically stable Singular Value Decomposition (or SVD) has played a major role in some of the activities centered around parameter estimation, especially when the signal is perturbed by some noise process which may or may not be known.; The main theme of this work is to identify specific speech application areas of subspace techniques and show that certain techniques are efficacious in the processing of speech signals. We will limit the scope of our topic to dealing with fundamental frequency (pitch) detection and estimation and enhancement of linear prediction (LP), a.k.a. autoregressive (AR) parameter estimation in the presence of additive white Gaussian noise (AWGN). We also develop a subspace centric view of white noise filtering and identify, explain, and offer a solution to the musical noise problem encountered with such techniques.; The methods presented are shown to enhance processing when the speech signal is immersed in AWGN of various proportions (measured according to signal-to-noise ratio). We show that speech quality for speech synthesis, when the source signal has added noise, can be improved by subspace-based enhancement and we perform Monte-Carlo simulations to provide insight into our claims. We also show that the variance of features extracted via low-rank, subspace-based processing will more closely approach the Cramer-Rao lower information bound of features extracted in the same manner when there is no noise present. These findings point the way to reduced variance in speech recognizers, for example, which will lead to better recognition performance when the recognition environment does not well match the training environment.