ALGORITHMS FOR PROCESSING FOURIER TRANSFORM PHASE OF SIGNALS

The studies presented in this thesis represent an attempt to process the Fourier transform (FT) phase of signals for feature extraction. Although the FT magnitude and phase spectra are independent functions of frequency features of a signal, most techniques for feature extraction from a signal are bked upon manipulating the the FT magnitude only. The phase spectrum of the signal corresponds to time delay corresponding to each of the sinusoidal components of the signal. In the context of additive noise, the time delay may not be significantly corrupted and the phase spectrum might be considered to be a more reliable source for estimating the features in a noisy signal. Although the importance of phase in signals is realised by researchers, very few attempts have been made to process the FT phase of signals for the extraction of features. Features of a signal, for example, resonance information, is completely masked by the inevitable wrapping of the phase spectrum. An alternative to processing the phase spectrum is processing the group delay function. The group delay function is the negative derivative of the (unwrapped) FT phase spectrum. The group delay function can be computed directly from the time domain signal.The group delay function possesses additive and high resolution properties, in that it shows a squared magnitude behaviour in the vicinity of a resonance. But the group delay function in general is not well behaved for all classes of signals. Zeros in the z-transform of a signal that are close to the unit circle cause large amplitude spikes to appear in the group delay function. The polarity of a spike depends on the location of the zero with respect to the unit circle. These large amplitude spikes mask the information about resonances. The research effort in this thesis focusses on the development of algorithms for manipulating the group delay function to suppress the information corresponding to the zeros of th signal that are close to unit circle in the z-domain and emphasise the features of of a signal. To demonstrate the usefulness of the algorithms developed, these algorithms are used to estimate (a) formant and pitch data from speech signals and ( b ) estimate spectra of auto-regressive processes and sinusoids in noise. The research effort in this thesis shows that the phase spectrum (or rather the group delay function) of a signal can be usefully processed to reliably extract features of a signal. ACKNOWLEDCEMENT I express my appreciation to Prof.B.Yegnanarayana for his constant help, excellent guidance and constructive criticisms throughout the course of this work. I thank Prof. R. ~a~arajan, Head, Department of Computer Science and Engineering, for making the various facilities in the department available to me: I owe my special thanks to Madhu Murthy and C.P.Mariadassou for some fruitful discussions. I thank G. V. Ramana Rao and R. Ramaseshan for reading my thesis and making useful suggestions. I would like to thank all my colleagues of the Speech and Vision Lab who have helped me in one way or the other. I thank Vatsala for providing me a shoulder whenever I was depressed. Finally, I thank my husband M. V. N. Murthy for his support and perseverence throughout the course of this work.