New Gabor wavelets with shift-invariance for improved time-frequency analysis and signal detection

We consider time-frequency detection and range-Doppler signal processing applications for wavelet processing; these differ considerably from the standard data representation and compression applications. In these cases, new wavelet functions and processing are necessary. We show that shift-invariance is essential (standard DWTs do not provide this), that dyadic scales are not sufficient, that wideband mother wavelet functions are necessary for some high noise cases and that small scale changes are generally required. A new Gabor wavelet implementation is described that is fast [O(N)], shift-invariant, flexible, and is not restricted to dyadic scales or to one basis function. It is compared to conventional dyadic DWTs, block shift-invariant DWTs, wavelet packets and other wavelet transform filter realizations requiring long filter sizes, large latency and long data buffers.