Multidimensional oversampled filter banks

Jianping Zhou; Minh N. Do

doi:10.1117/12.618209

17 September 2005 Multidimensional oversampled filter banks

Jianping Zhou, Minh N. Do

Proceedings Volume 5914, Wavelets XI; 591424 (2005) https://doi.org/10.1117/12.618209
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

We present the characterization and design of multidimensional oversampled FIR filter banks. In the polyphase domain, the perfect reconstruction condition for an oversampled filter bank amounts to the invertibility of the analysis polyphase matrix, which is a rectangular FIR matrix. For a nonsubsampled FIR filter bank, its analysis polyphase matrix is the FIR vector of analysis filters. A major challenge is how to extend algebraic geometry techniques, which only deal with polynomials (that is, causal filters), to handle general FIR filters. We propose a novel method to map the FIR representation of the nonsubsampled filter bank into a polynomial one by simply introducing a new variable. Using algebraic geometry and Groebner bases, we propose the existence, computation, and characterization of FIR synthesis filters given FIR analysis filters. We explore the design problem of MD nonsubsampled FIR filter banks by a mapping approach. Finally, we extend these results to general oversampled FIR filter banks.

Citation Download Citation

Jianping Zhou and Minh N. Do "Multidimensional oversampled filter banks", Proc. SPIE 5914, Wavelets XI, 591424 (17 September 2005); https://doi.org/10.1117/12.618209

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