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Novel time-frequency analysis techniques are proposed§for deterministic signals. We show that among all§linear time-frequency representations only the§short-time Fourier transformation (STFT) family §satisfies both the shift-invariance and§rotation-invariance properties in time,§frequency and all fractional Fourier domains. The§time-frequency domain localization by STFT is§characterized by introducing a novel generalized§time-bandwidth product (GTBP) definition, which is an§extension of the time-bandwidth product on the§fractional Fourier domains. GTBP provides a§rotation-independent measure of compactness for§mono-component signals. The GTBP optimal STFT is a§well-localized and high resolution time-frequency§representation providing optimal results for§chirp-like signals that are encountered§in a variety of application areas including radar,§sonar, seismic, and biological signal processing. An§improved GTBP optimal STFT analysis is obtained for§signals with non-convex time-frequency support and§its computationally efficient form is presented.§Finally, we extend these ideas from time-frequency§distributions to joint fractional Fourier domain§representations.
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