Fast Approach for Analysis Windows Computation of Multiwindow Discrete Gabor Transform

By using the biorthogonal analysis approach, an effective algorithm based on factorization for solving the analysis/dual windows in multiwindow discrete Gabor transform (M-DGT) is presented for arbitrary given synthesis windows. The constraint condition matrix of the M-DGT between analysis/dual windows and synthesis windows is proved to be equivalent to a fixed number of independent orthogonal relationship matrixes of discrete Gabor transform (DGT), which can be quickly and efficiently solved by using sub-equation sets. The analysis and comparison of computational complexity of related algorithms have indicated that the proposed algorithm provided a faster computational approach for computing analysis/dual windows as compared with that of the existing algorithms, which can save amount of computation and memory.