ON THE STUDY OF 4-PARALLELOGRAM FILTER BANKS

The most commonly used 2-D filter banks are separable filter banks, wh ich 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 separ able systems are unions of four rectangles. The natural nonseparable g eneralization of such supports are those that are unions of four paral lelograms. In this paper, we study four parallelogram filter banks, wh ich is the class of 2-D filter banks in which the supports of the anal ysis and synthesis filters consist of four parallelograms. For a given a decimation matrix, there could be more than one possible configurat ion (the collection of passbands of the analysis filters). Various typ es 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. The will see t hat there is only one category of these filter banks. The configuratio ns of four-parallelogram filter banks in this category can always be a chieved by designing filter banks of low design cost.