THE RATIO SPECTRUM: THEORY, APPLICATIONS AND ANALOG IMPLEMENTATION By LIPING DENG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE RATIO SPECTRUM: THEORY, APPLICATIONS AND ANALOG IMPLEMENTATION By Liping Deng May 2002 Chairman: Dr. John G. Harris Major Department: Electrical and Computer Engineering The power spectrum is fundamental to signal analysis and understanding and has found many applications in communications, speech, and radar. One of the disadvantages of using the power spectrum is that the estimate of the power spectrum is inconsistent, meaning that the variance of the estimate does not approach zero even when the data length grows infinitely large. Lim and Harris have developed a simple analog IC for Ratio Spectrum (RS) computation. The RS is formed by computing the ratio of the power of a low-pass filtered signal to the power of the original un-filtered signal for all possible filter cutoff frequencies. The RS has many advantages over the traditional power spectrum, particularly in terms of improved feature extraction and efficient implementation in analog circuitry. We first study the important result that the integrated spectrum and the ratio spectrum are consistent estimators unlike the widely used power spectrum. This property makes the integrated spectrum and the ratio spectrum more useful for some applications than the