A Unified Framework for Synthesis of Cosine-Modulated Filter Banks and Corresponding Wavelets

Abstract

By directly optimizing the impulse response coefficient of filter banks, the synthesis of cosine-modulated FIR filter banks and cosine-modulated wavelets can be carried out in a unified framework. Through proper transformation, the problem is formulated as a quadratic-constrained least-squares (QCLS) minimization problem where all constraint matrices are symmetric and positive definite. Furthermore, we create an analog neural network by the augmented cost of the QCLS problem for designing filter banks and wavelets in real time. It turns out that the analysis and synthesis filters with high stopband attenuation and compactly supported wavelets are easily obtained by this method. Computer simulations illustrated the efficiency and effectiveness of our method.KeywordsFilter BankPerfect ReconstructionPrototype FilterSynthesis FilterStopband AttenuationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.