Optimal Design of Oversampled Synthesis FBs With Lattice Structure Constraints

• Published in: IEEE transactions on signal processing Vol. 59; no. 8; pp. 3549 - 3559
• Main Authors: Chai, Li, Zhang, Jingxin, Sheng, Yuxia
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Correlation; Design methodology; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Lattice structure; Lattices; Linear phase; Mathematical models; Noise; Noise reduction; Optimization; oversampled filter banks; Parametrization; perfect reconstruction; Reduction; Signal and communications theory; Signal, noise; Symmetric matrices; Synthesis; Telecommunications and information theory; Performance evaluation; Subband decomposition; Noise reduction; perfect reconstruction; Linear phase; Oversampling; Parameterization; Implementation; Optimal design; Truss structure; Optimal solution; Signal processing; Numerical simulation; Filter bank; Lattice structure; Phase reconstruction; oversampled filter banks
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2147783

Oversampled filter banks (FBs) with lattice structure allow fast implementation and guarantee the linear phase and perfect reconstruction property. For such FBs, the synthesis FB is not unique. This nonuniqueness provides extra design freedom for optimal reduction of subband noise required in many applications. However, the existing design methods of synthesis FB for optimal reduction of subband noise cannot guarantee the linear phase and lattice structure property. This paper studies the design of oversampled synthesis FBs with guaranteed lattice structure for optimal reduction of subband noise. Based on a state space parameterization of all synthesis FBs with lattice structure, the explicit formulae are derived to find the optimal solution for noise reduction. Numerical examples are presented to demonstrate the effectiveness of the new design methods obtained.