Maximally Decimated Paraunitary Linear Phase FIR Filter Bank Design via Iterative SVD Approach

• Published in: IEEE transactions on signal processing Vol. 63; no. 2; pp. 466 - 481
• Main Authors: Ling, Bingo Wing-Kuen, Nili Tian, Ho, Charlotte Yuk-Fan, Wan-Chi Siu, Kok-Lay Teo, Qingyun Dai
• Format: Journal Article
• Language: English
• Published: New York IEEE 15-01-2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical solution; Banks; CAD; Computer aided design; Computer simulation; Filter banks; Finite impulse response filters; FIR filters; Lattices; Linear phase; M -channel maximally decimated paraunitary linear phase FIR least squares filter bank design; Mathematical analysis; Mathematical models; Matrix decomposition; Optimization; orthogonal Procrustes optimization; Singular value decomposition; Sufficient conditions
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2371779

A necessary and sufficient condition for M-channel maximally decimated paraunitary FIR filter banks is derived when the lengths of all the filters are the same and they are integer multiples of M. Based on the derived condition, a family of this kind of filter banks is defined. These results are also applied to the corresponding linear phase filter banks. Then, the design of this type of filter banks with the linear phase property is formulated as two orthogonal Procrustes optimization problems. The analytical solution of each optimization problem is derived based on a singular value decomposition approach. Since no numerical optimization computer aided design tool is required for finding the analytical solution of each optimization problem, the computational power required for our proposed method is much lower than that for existing methods. Computer numerical simulation results show that our proposed method can obtain a design instantaneously.