On the study of four-parallelogram filter banks

Yuan-Pei Lin*, P. P. Vaidyanathan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The most commonly used 2-D filter banks are separable filter banks, which can be obtained by cascading two 1-D filter banks in the form of a tree. The supports of the analysis and synthesis filters in the separable systems are unions of four rectangles. The natural nonseparable generalization of such supports are those that are unions of four parallelograms. In this paper, we study four parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of four parallelograms. For a given a decimation matrix, there could be more than one possible configuration (the collection of passbands of the analysis filters). Various types of configuration will be constructed for four-parallelogram filter banks. Conditions on the configurations will be derived such that good design of analysis and synthesis filters are possible. We will see that there is only one category of these filter banks. The configurations of four-parallelogram filter banks in this category can always be achieved by designing filter banks of low design cost.

Original languageEnglish
Pages (from-to)2707-2717
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number11
StatePublished - 1 Dec 1996

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