Multidimensional FIR filter design by transformation

Lina Karam

Research output: Contribution to journalArticlepeer-review


The McClellan transformation is an efficient and popular method for designing multidimensional FIR filters by transforming onedimensional (1D) FIR prototype filters. This paper extends the McClellan transformation method so that new types of 1D filters can be transformed, and new types of multidimensional filters can be designed. For this purpose, a new expression for the frequency response of an arbitrary 1D filter is derived in terms of Chebyshev polynomials as well as other introduced polynomials satisfying recurrence formulae. The main objective is to identify which prototype filters can be transformed, determine what types of symmetry can be designed, and present procedures for transforming the new identified prototypes as well as rules for achieving the possible symmetries. Two efficient procedures are presented for the design of complex and real, positive and negative symmetric multidimensional filters by transforming 1D prototype filters with complex (or real) coefficients. The first procedure is used to design complex multidimensional filters with a rectangular region of support having oddlength sides, whereas the second procedure is used for filters with a rectangular region of support having evenlength sides. The designed filters can be implemented efficiently using special Chebyshev structures. Design examples are presented to illustrate the performance of the design procedures.

Original languageEnglish (US)
Number of pages1
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Dec 1 1997

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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