Efficient design of very large-scale DFT modulated filter banks using Mth band condition

This study presents several new properties of the discrete Fourier transform (DFT) modulated filter banks and efficient algorithm for designing the filter banks with very large-scale (with a very large number of subbands and very long filters). For DFT modulated filter bank, the authors derive the symmetric property of the overall transfer function and aliasing transfer functions which can be efficiently calculated by using the orthogonal property of the DFT matrix. By invoking the Mth band condition and new property, an efficient algorithm is proposed to design DFT modulated filter banks. The convergence of the algorithm is also proved. Several numerical examples and comparison with the conventional methods are included to show the effectiveness of the proposed algorithm.