Characterizations of Bidimensional Filters

Let A be a 2 times 2 expansive matrix with integer entries and |detA| = 2. Let h₀ E (AT)^-1Z²/Z², and m is a 2piZ² periodic 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.