Optimal representation of transient biological signals using the adaptive Gabor transform.

Signal analysis is the process by which a signal is transformed into a representation which is meaningful and informative. The observed signal is often a complex manifestation of a simple generating system. Frequency analysis provides an easy to interpret signal representation for signals consisting of sums of sinusoids. Time-varying signals such as speech consist of sinusoidal elements which change in frequency and intensity with time. Frequency analysis is inadequate for describing these signals because it can only indicate what frequencies are present in the signal, not when they occurred. Joint time-frequency analyses capture the spectral dynamics of these time-varying signals and are useful tools for visual signal analysis. However, a characterization of a signal's time-frequency distribution using a small number of parameters is required for pattern classification problems. A parametric time-frequency representation that captures quantitatively the important time-frequency features of signals which are compactly supported in time-frequency space has been developed. This analysis technique is called the Adaptive Gabor Transform (AGT). The AGT represents a signal as a linear combination of Gaussian modulated sinusoids called Gabor logons. These logons are parameterized by time, frequency, spread, phase, chirp rate and amplitude. D. Gabor first suggested representing signals as a linear combination of fixed shape Gabor logons modulated and time-shifted by discrete time and frequency intervals. The Gabor transform uses fixed shape basis functions on a fixed rectangular time-frequency grid in order to gain computational efficiency. However, computational efficiency is gained at the expense of representational efficiency. The AGT provides an efficient representation of signals which are compactly supported in time-frequency space. For example, temporomandibular joint sounds are almost perfectly reconstructed (correlation coefficient of 0.99) from a single Gabor logon. The AGT has been used to analyze event-related potentials (ERPs) collected as part of a psychiatry experiment. The AGT was able to fit the ERPs well (average correlation coefficient of 0.83). Significant classification of the ERPs according to stimulus category was achieved on the basis of the AGT parameters (t(11) = 2.71, $p \le 0.02).$.PhDBioengineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103911/1/9423148.pdfDescription of 9423148.pdf : Restricted to UM users only