Optimal biorthogonal analysis window function for discrete Gabor transform
Shie Qian, Dapang Chen · IEEE Transactions on Signal Processing · 1994
Like the DFT/spl minus/a discrete version of the Fourier transform/spl minus/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 /spl gamma/(i) is not unique. The authors discuss the solution of /spl gamma/(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 /spl gamma//sub 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.>