Generalized method for improving the STFT via Linear Canonical Transforms

It has been previously shown that chirp signals can be manipulated into a minimal time-bandwidth product (TBP) form in its so called natural domain, via fractionally Fourier transforming. Here we show that the time-bandwidth product (TBP) of the signal can be achieved in various other ways, under the class of Linear Canonical Transforms (LCT), which can be decomposed into shearing operations in time and frequency of the energy support of the signal. A general background on LCT is built, and its possible uses for obtaining the GTBP are presented.