A general formulation of modulated filter banks

Peter Niels Heller, Tanja Karp, Truong Q. Nguyen

Research output: Contribution to journalArticlepeer-review

145 Scopus citations

Abstract

This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation - modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).

Original languageEnglish
Pages (from-to)986-1002
Number of pages17
JournalIEEE Transactions on Signal Processing
Volume47
Issue number4
DOIs
StatePublished - 1999

Keywords

  • Cosine-modulated filter bank
  • DCT
  • Filter bank
  • MDCT
  • Modulated filter bank

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