Parallel Lattice Structure for Dual Windows Computation in Multiwindow Gabor Transform

The multiwindow discrete Gabor transform (M-DGT) is a useful time-frequency analysis tool for non-stationary signal processing. Given an arbitrary Gabor frame, a parallel lattice structure of block time-recursive algorithm for fast and efficient computation of dual/analysis Gabor windows for M-DGT is presented. By using a multiple window dual Gabor frame, the dual Gabor windows can be expressed by synthesis and analysis windows with a block-circulant matrix. Then, a parallel lattice structure of block time-recursive can be derived to solve the dual Gabor windows by the block-circulant matrix computed by the fast discrete Fourier transform (FFT). When compared to three existing methods, the proposed algorithm can reduce computational complexity and save computational time. Experimental results indicate that the proposed algorithm is valid to compute the dual windows of the M-DGT, which make the algorithm attractive for fast time-frequency signal analysis and processing.