Structure simplification of nonrecursive 2-D digital filters: a new L∞ error bound

This brief presents an error analysis for the SVD-based structure simplification method. Specifically, we derive a new L_∞ error bound for the simplification strategy. The error bound obtained is very tight as compared to the existing bound. The significance of having such a bound is twofold. First, if the frequency response of the original function is satisfactory and the error bound obtained is small, then there will be no spikes for the frequency response of the simplified transfer function over the entire baseband. Second, a tight bound serves as a guide to determine how many parallel sections can be neglected from the filter network without exceeding a prescribed tolerance. The new error bound therefore offers an additional justification for the use of the SVD-based simplification technique. An example is included to illustrate the algorithm for computing the error bound and demonstrate the tightness of the bound