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TitleOptimal design of synthesis filters in multidimensional perfect reconstruction FIR filter banks using Gröbner bases
Author(s) Hyungju Park
TypeArticle in Journal
AbstractFor a given low-pass analysis filter in an n-dimensional (n-D) perfect reconstruction (PR) FIR filter bank, there exists certain degree of freedom in designing a synthesis filter to make the overall filter bank have PR property, and Quillen-Suslin Theorem can be used to precisely determine the degree of freedom. Designing a PR synthesis filter with optimal frequency response amounts to minimizing the deviation between the frequency responses of the synthesis filter and an ideal filter under the PR constraint. In this paper, a method based on Grobner bases computation is developed for optimally designing critically sampled n-D PR FIR filter banks when one analysis filter is known. This design method can be easily combined with various existing design methods including minimax optimization and weighted least squares optimization, and can incorporate additional design goals including linear phase and bandpass characteristic.
KeywordsElectric network synthesis, Frequency response, Optimization, Least squares approximations, Z transforms, Polynomials, Signal filtering and prediction, Algorithms
URL dx.doi.org/10.1109/TCSI.2002.1010039
JournalIEEE Transactions on Circuits and Systems I
SeriesFundamental Theory and Applications
Translation No
Refereed No