Characterizations of Bidimensional Filters
Zhongyan Li, Chunlei Shi, Yuanyuan Shi · 2009
Let A be a 2 times 2 expansive matrix with integer entries and |detA| = 2. Let h0E (AT)-1Z2/Z2, and m is a 2piZ2periodic function, m is called an A-dilation generalized filter if it satisfies |m(s)|2+ |m(s + 2pih0)|2 = 1, for any s isin R2, where R is the real number set and Z is the integer set. In this paper, we discuss these filters. We present a concrete constructing method of such a filter, and give some equivalent conditions of an A-dilation generalized filter being an A-dilation low pass filter of some Multiresolution Analysis.