THE WIGNER DISTRIBUTION AND THE AMBIGUITY FUNCTION: GENERALIZATIONS, ENHANCEMENT, COMPRESSION AND SOME APPLICATIONS (SIGNAL PROCESSING, PATTERN RECOGNITION, COMPUTER VISION, MEDICAL ULTRASONICS)

Focus of this research is on two generic time-frequency signal representations--the Wigner distribution (WD) and the ambiguity function (AF). As a generalization, to make these tools available for scale-invariant signal processing and for characterization of scale-invariant systems, they are suitably redefined. The properties of the resulting scale-invariant WD and AF are analyzed in detail. Their potential applications for the scale-invariant processing of 1-D and 2-D signals and analysis of the 1-D and 2-D scale-invariant systems are discussed.;In a medical ultrasound application, use of the singular value spectrum enables efficient estimation of the frequency shift along a region in the reflecting tissue. This is necessary for accurate measurement of the ultrasonic attenuation in tissue--a very extensively studied problem, but without much success. In another application, spectrum coefficients provide very good descriptors of shape that satisfy all standard requirements and with good noise immunity. Using the simple procedures successful classification of planar shapes is achieved.;The issues of data compression, enhancement and new applications of the conventional WD and AF are studied. It is shown that the WD provides insight into the filtering action of the linear systems that is not available with conventional approaches. An outer product expansion was proposed and used for enhancement of the WD. This provides for improved parameter estimation and detection of signals in the time-frequency plane. A new, non-linear, non-unitary signal transformation is proposed. It is generated by the singular value decomposition of either WD or ambiguity function. Resulting set of singular values is the same in both cases and it defines a generalized "spectrum" of the signal. The properties of this singular value spectrum are shown to be correlated with the important physical characteristics of the signal. This is a consequence of the fact that representation of signals in time-frequency plane encodes more explicitly certain signal features, such as its time-bandwidth product, the complexity of frequency vs. time variation, and the complexity of signals in terms of the number of components and their spacing. The transformation of the signal into its singular value spectrum seems to be a rather powerful tool for variety of signal processing applications. Two different applications of this spectrum are explored.