A Design of Near Perfect Reconstruction Linear-Phase QMF Banks Based on Hybrid Steepest Descent Method

Hiroshi HASEGAWA  Isao YAMADA  Kohichi SAKANIWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.8   pp.1523-1530
Publication Date: 2000/08/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Filter Banks
Keyword: 
two-channel linear phase FIR QMF bank,  near perfect reconstruction,  convex projection technique,  hybrid steepest descent method,  magnitude product space,  

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Summary: 
In this paper, we propose a projection based design of near perfect reconstruction QMF banks. An advantage of this method is that additional design specifications are easily implemented by defining new convex sets. To apply convex projection technique, the main difficulty is how to approximate the design specifications by some closed convex sets. In this paper, introducing a notion of Magnitude Product Space where a pair of magnitude responses of analysis filters is expressed as a point, we approximate design requirements of QMF banks by multiple closed convex sets in this space. The proposed method iteratively applies a convex projection technique, Hybrid Steepest Descent Method, to find a point corresponding to the optimal analysis filters at each stage, where the closed convex sets are dynamically improved. Design examples show that the proposed design method leads to significant improvement over conventional design methods.