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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