Optimal Design of Cosine Modulated Nonuniform Linear Phase FIR Filter Bank via Both Stretching and Shifting Frequency Response of Single Prototype Filter

• Published in: IEEE transactions on signal processing Vol. 62; no. 10; pp. 2517 - 2530
• Main Authors: Ling, Bingo Wing-Kuen, Ho, Charlotte Yuk-Fan, Kok-Lay Teo, Wan-Chi Siu, Jiangzhong Cao, Qingyun Dai
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 15.05.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computer simulation; Cosine modulated nonuniform linear phase finite impulse response filter bank; Design engineering; Detection, estimation, filtering, equalization, prediction; direct design; Exact sciences and technology; Filter banks; Finite impulse response filters; global nonconvex functional inequality constrained optimization; Hearing aids; Information filtering; Information, signal and communications theory; joint constraint transcription and modified filled function method; Mathematical analysis; Mathematical models; Maximum likelihood detection; Modulation, demodulation; Nonlinear filters; Nonuniform; Optimization; Prototypes; Queuing theory; Signal and communications theory; Signal, noise; stretching and shifting the frequency response; Telecommunications and information theory; Performance evaluation; Non convex programming; Prototype; Computer simulation; Linear phase; joint constraint transcription and modified filled function method; Specification; Optimal design; Constrained optimization; Digital filter; Linear phase filters; Aliasing; Cosine modulated nonuniform linear phase finite impulse response filter bank; Modulation; Optimal solution; Signal processing; direct design; Finite impulse response filter; Numerical simulation; Filter bank; Frequency response; Error correction; global nonconvex functional inequality constrained optimization; stretching and shifting the frequency response
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2312326

This paper designs an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of a single prototype filter. The total aliasing error of the filter bank is minimized subject to specifications on the maximum magnitude distortion of the filter bank and the maximum ripple magnitudes of the prototype filter over both the passband and the stopband. This paper proposes a joint constraint transcription and modified filled function method for solving the optimization problem. In particular, the functional inequality constraints are converted to discrete constraints via the constraint transcription method. The globally optimal solution of the nonconvex optimization problem can be found efficiently via the modified filled function method. Computer numerical simulation results show that our design outperforms existing designs.