Critically sampled Gabor transform with localized biorthogonal function

A new implementation of the critically sampled nonperiodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the propsed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biorthogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is the non-localization of the resultant biorthogonal function. A fast algorithm to compute the derived biorthogonal function is proposed