Time-Frequency Analysis Buchkatalog

Novel time-frequency analysis techniques are proposedfor deterministic signals. We show that among alllinear time-frequency representations only theshort-time Fourier transformation (STFT) family satisfies both the shift-invariance androtation-invariance properties in time, frequency and all fractional Fourier domains. Thetime-frequency domain localization by STFT ischaracterized by introducing a novel generalizedtime-bandwidth product (GTBP) definition, which is anextension of the time-bandwidth product on thefractional Fourier domains. GTBP provides arotation-independent measure of compactness formono-component signals. The GTBP optimal STFT is awell-localized and high resolution time-frequencyrepresentation providing optimal results forchirp-like signals that are encounteredin a variety of application areas including radar, sonar, seismic, and biological signal processing. Animproved GTBP optimal STFT analysis is obtained forsignals with non-convex time-frequency support andits computationally efficient form is presented.Finally, we extend these ideas from time-frequencydistributions to joint fractional Fourier domainrepresentations.