 
Summary: Symmetric Extension for
TwoChannel Quincunx Filter Banks
Yi Chen, Michael D. Adams, and WuSheng Lu
Department of Electrical and Computer Engineering
University of Victoria
Abstract
In the case of onedimensional filter banks, symmetric ex
tension is a commonly used technique for constructing non
expansive transforms of finitelength sequences. In this pa
per, we show how symmetric extension can be extended to
the case of twodimensional filter banks based on quincunx
sampling. In particular, we show how, for filter banks of this
type, one can construct nonexpansive transforms for input
sequences defined on arbitrary rectangular regions.
1. Introduction
Fig. 1 shows a twodimensional twochannel filter bank. Of
ten, such a filter bank is defined so as to operate on se
quences of infinite extent. In practice, however, we always
deal with sequences of finite extent. Therefore, we usu
ally require some means for adapting filter banks to such
