Modern Methods of Time-Frequency Warping of Sound Signals

Tato práce se zabývá reprezentací nestacionárních harmonických signálů s časově proměnnými komponentami. Primárně je zaměřena na Harmonickou transformaci a jeji variantu se subkvadratickou výpočetní složitostí, Rychlou harmonickou transformaci. V této práci jsou prezentovány dva algoritmy využívající Rychlou harmonickou transformaci. Prvni používá jako metodu odhadu změny základního kmitočtu sbírané logaritmické spektrum a druhá používá metodu analýzy syntézou. Oba algoritmy jsou použity k analýze řečového segmentu pro porovnání vystupů. Nakonec je algoritmus využívající metody analýzy syntézou použit na reálné zvukové signály, aby bylo možné změřit zlepšení reprezentace kmitočtově modulovaných signálů za použití Harmonické transformace.This thesis deals with representation of non-stationary harmonic signals with time-varying components. Its main focus is aimed at Harmonic Transform and its variant with subquadratic computational complexity, the Fast Harmonic Transform. Two algorithms using the Fast Harmonic Transform are presented. The first uses the gathered log-spectrum as fundamental frequency change estimation method, the second uses analysis-by-synthesis approach. Both algorithms are used on a speech segment to compare its output. Further the analysis-by-synthesis algorithm is applied on several real sound signals to measure the increase in the ability to represent real frequency-modulated signals using the Harmonic Transform.

Fractional Focusing and the Chirp Scaling Algorithm With Real Synthetic Aperture Radar Data

abstract: For synthetic aperture radar (SAR) image formation processing, the chirp scaling algorithm (CSA) has gained considerable attention mainly because of its excellent target focusing ability, optimized processing steps, and ease of implementation. In particular, unlike the range Doppler and range migration algorithms, the CSA is easy to implement since it does not require interpolation, and it can be used on both stripmap and spotlight SAR systems. Another transform that can be used to enhance the processing of SAR image formation is the fractional Fourier transform (FRFT). This transform has been recently introduced to the signal processing community, and it has shown many promising applications in the realm of SAR signal processing, specifically because of its close association to the Wigner distribution and ambiguity function. The objective of this work is to improve the application of the FRFT in order to enhance the implementation of the CSA for SAR processing. This will be achieved by processing real phase-history data from the RADARSAT-1 satellite, a multi-mode SAR platform operating in the C-band, providing imagery with resolution between 8 and 100 meters at incidence angles of 10 through 59 degrees. The phase-history data will be processed into imagery using the conventional chirp scaling algorithm. The results will then be compared using a new implementation of the CSA based on the use of the FRFT, combined with traditional SAR focusing techniques, to enhance the algorithm's focusing ability, thereby increasing the peak-to-sidelobe ratio of the focused targets. The FRFT can also be used to provide focusing enhancements at extended ranges.Dissertation/ThesisM.S. Electrical Engineering 201