Nonstationary Signal Processing with Application to Reverberation Cancellation in Acoustic Environments

In this age of instantaneous world-wide telecommunication, the demands on speech quality and intelligibility from devices such as the mobile telephone, tele-conferencing systems and even the hearing aid are dramatically increasing. It is often expected that these devices will produce `Compact Disc' quality sound and certainly that the presence of any background noise will be suppressed. However, the degradation in the quality and intelligibility of the received speech is constrained by the acoustical properties of the environment in which the audio signal is acquired. In any confined environment, the sound heard by a person is not simply the original emitted sound, but the combination of a series of an enormous number of echoes from different surfaces: the process of reverberation.

A considerable number of linear signal processing problems reduce to the fundamental tasks of signal separation and deconvolution. A large proportion of these problems are blind in the sense that neither of the source signals are known, and this substantially increases the difficulty of the problem. It is, therefore, of considerable interest to solve the problems of single channel signal separation and single channel blind deconvolution (also known as blind dereverberation).

This dissertation is arranged in two parts. First, the problem of determining separability criteria and achieving signal separation is considered. Separability of signal mixtures, given only one mixture observation, is defined as the identification of the accuracy to which signals can be separated. The work introduces a signal separation technique by concatenating the domains on which two signal classes can be represented with a finite number of basis functions. The separation of uniformly modulated signals is considered, and an example of separating chirp signals embedded in multiplicative noise is given. The second part of this dissertation considers single channel blind deconvolution, in which a degraded observed signal is modelled as the convolution of a nonstationary source signal with a stationary distortion operator. Recovery of the source signal from the observed signal is achieved by modelling the source signal as a time-varying autoregressive process, the distortion operator by a IIR filter, and then using a Bayesian framework to estimate the parameters of the distorting filter, which can be used to deconvolve the observed signal. A further generalisation of this model using subband techniques is introduced.

Throughout the dissertation, the philosophy of how the nonstationary properties of the source signal allow the identification of the interference or distortion operator to be uniquely determined is discussed.