Efficient Design of High-Complexity Cosine Modulated Filter Banks Using $2 M$th Band Conditions
Zijing Zhang, Peng‐Lang Shui, Tao Su · IEEE Transactions on Signal Processing · 2008
This paper presents several new properties of biorthogonal cosine modulated filter banks (CMFBs) and efficient algorithms for designing CMFBs with a very large number of subbands and very long filters. For a biorthogonal CMFB, we find the periodicity and symmetry of its overall transfer function and aliasing transfer functions which can be efficiently computed based on a decimated uniform discrete Fourier transform (DFT) analysis filter bank. By exploiting gradient information and$2 M$th band conditions, efficient algorithms are proposed for designing both orthogonal and biorthogonal CMFBs. In addition, an efficient matrix inversion algorithm with$O(N^{2} )$complexity is also presented. Several numerical examples and comparisons with many other existing methods are included to demonstrate the design performance and efficiency of the algorithms.