In this thesis novel time frequency analysis techniques are proposed for deterministic signals It is shown that among all linear time frequency representations only the short time Fourier transformation STFT family satis es both the shift invariance and rotation invariance properties in both time frequency and all fractional Fourier domains The time frequency domain localization by STFT is then characterized by introducing a novel generalized time bandwidth product GTBP de nition which is an extension of the time bandwidth product TBP on the fractional Fourier domains For mono component signals it is shown that GTBP provides a rotation independent measure of compactness The GTBP optimal STFT which is a well localized and high resolution time frequency representation is introduced and its computationally e cient form is presented The GTBP optimal STFT provides optimal results for chirp like signals which can be encountered in a variety of application areas including radar sonar seismic and biological signal processing Also a linear canonical decomposition of the GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT Furthermore for signals with non convex time frequency support an improved GTBP optimal STFT analysis is obtained through chirp multiplication or equivalently shearing in the D time frequency domain Finally we extend these ideas from time frequency distributions to joint fractional Fourier domain representations