Asymptotic stability of two-dimensional digital filters under quantization

The stability of 2-D digital filters implemented with two's complement quantization is investigated. The difference equation model is considered for the following cases: (i) quantization after each product and (ii) quantization after a complete sum of products. For both cases, sufficient conditions are established for asymptotic stability. The 2-D state-space Roesser's (1975) model is also considered under two's complement quantization, and a sufficient condition is derived for its stability. Some examples are given to illustrate the results.<
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