Optimal biorthogonal analysis window function for discrete Gabor transform

Like the DFT-a discrete version of the Fourier transform-the recently developed discrete Gabor transform (DGT) provides a feasible vehicle to implement the very useful Gabor expansion. In general, the choice of the biorthogonal window function γ(i) is not unique. The authors discuss the solution of γ(i) that is optimally close to an arbitrary desired function d(i) when the synthesis window h(i) and sampling pattern are given. For d(i)=h(i), the resulting γ_opt (i) directly leads to so-called orthogonal-like DGT. Combining the DGT, they believe that the result presented in this paper is rather significant for digital signal processing