 
Summary: SYMMETRIC EXTENSION FOR TWOCHANNEL QUINCUNX FILTER BANKS
Yi Chen, Michael D. Adams, and WuSheng Lu
Dept. of Elec. and Comp. Eng., University of Victoria, Victoria, BC, CANADA
ABSTRACT
In the case of onedimensional filter banks, symmetric extension is
a commonly used technique for constructing nonexpansive trans
forms of finitelength sequences. In this paper, we show how sym
metric 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 re
gions.
1. INTRODUCTION
The twodimensional (2D) twochannel filter bank shown in Fig. 1
can be used to compute a class of transforms that has proven ex
tremely useful in many image processing applications. Often, such
a filter bank is defined so as to operate on sequences of infinite
extent. In practice, however, we almost invariably deal with se
quences of finite extent. Therefore, we usually require some means
for adapting filter banks to such sequences. This leads to the well
