A new criterion is derived that relates the stability of two-dimensional recursive filters to the properties of its cepstrum. It provides a procedure for the decomposition of unstable recursive filters having nonzero, nonimaginary frequency response into stable recursive filters. The optimal solution of the decomposition problem is discussed, including numerical implementation and nonrecursive solutions. Several numerical examples show the potentialities and limitations of the rules for decomposition and for truncation of the operators.
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