Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming

• Published in: IEEE transactions on signal processing Vol. 53; no. 7; pp. 2598 - 2603
• Main Authors: Ho, C.Y.-F., Bingo Wing-Kuen Ling, Yan-Qun Liu, Tam, P.K.-S., Kok-Lay Teo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bandwidth; Crosstalk; Design methodology; Distortion; Dual parameterization; Filtering theory; Finite impulse response filter; Frequency domain analysis; Impulse response; Mathematical analysis; Nonuniform; nonuniform transmultiplexer; Optimization; Passband; Programming; Quadratic programming; Ripples; semi-infinite programming; Signal processing; Signal processing algorithms; Specifications
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2005.849209

This correspondence considers an optimum nonuniform finite impulse response (FIR) transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique, and the local solution is a global minimum.