Time-frequency signal representation with Dopplerlet basis functions

A new time frequency signal representation called Dopplerlet transform is presented to overcome the deficiency of basis functions with linear time frequency relations. Physical analysis and theoretical predictions indicate that the proposed transform essentially performs a nonlinear segmentation of the time frequency energy distribution, as opposed to many other transforms characterized by linear segmentation such as the Fourier transform, short time Fourier transform (including the Gabor transform), wavelet transform and chirplet transform which are all special cases of the Dopplerlet transform with specific parameters. Matching pursuits are used to decompose the signal into Dopplerlet basis functions which best match the signal components, so the signal can be reconstructed using as few waveforms as possible. A new concept, the “pseudo time frequency distribution” is proposed which resolutes both time and frequency domains to their theoretical limits.