THE GENERALIZED GABOR TRANSFORM

The generalized Gabor transform is discussed. For a given function f(t ), t is an element of R, the generalized Gabor transform finds a set o f coefficients a(mr) such that GRAPHICS The original Gabor transform proposed by D, Gabor 1 is the special case of T = T', The computati on of the generalized Gabor transform with biorthogonal functions is d iscussed. The optimal biorthogonal functions are discussed, A relation between a window function and its optimal biorthogonal function is pr esented based on the Zak transform when T/T' is rational. The finite d iscrete generalized Gabor transform is also derived. Methods of comput ation for the biorthogonal function are discussed. The relation betwee n a window function and its optimal biorthogonal function derived for the continuous variable generalized Gabor transform can be extended to the finite discrete case. Efficient algorithms for the optimal biorth ogonal function and generalized Gabor transform for the finite discret e case are proposed.