Multidimensional oversampled filter banks

Jianping Zhou, Minh N Do

Research output: Contribution to journalConference articlepeer-review


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 Gröbner 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.

Original languageEnglish (US)
Article number591424
Pages (from-to)1-12
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2005
EventWavelets XI - San Diego, CA, United States
Duration: Jul 31 2005Aug 3 2005


  • Filter banks
  • Finite impulse response (FIR)
  • Matrix inverse
  • Multidimensional
  • Nonsubsampled
  • Oversampled
  • Perfect reconstruction
  • Polyphase

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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