New limit cycle bounds for digital filters

Tighter limit cycle bounds for digital filters

“…In order to provide an objective comparison, we have employed the same set of digital filters included in [9] to compare the bounds derived along these lines with those from previous studies. For convenience, Table I shows the filters specifications, and we include in Table II the resulting equivalent -matrix.…”

“…For convenience, Table I shows the filters specifications, and we include in Table II the resulting equivalent -matrix. The flowgraphs for the structures appear in [9,. Table III presents the results obtained working with four different methods.…”

“…It shows the zero-input limit cycle bounds, corresponding to each delay element , of the three filters analyzed. The abbreviation YP refers to Yakowitz and Parker bounds presented in [8], GMN indicates the general bounds described in [9] by Green and Turner, and CMN the computational bounds also presented in the same reference by Green and Turner. Finally, the last column holds the new bounds (NB) obtained working with the procedure presented in this letter.…”

“…However, considering the maximum number of vectors to test (35) in the exhaustive search, NB bounds are always better. The procedure required to obtain CMN bounds involves a rather complex maximization problem, which is difficult to implement and highly time consuming [9]. On the other hand, NB bounds can be computed in negligible time and are quite easy to program, for example, using MATLAB.…”

Systematic ultimate bound computation for sampled-data systems with quantization

“…However, statistical description of the quantization error may lead to unnecessary difficulties if only a guaranteed ultimate bound is sought. Methods that employ a deterministic framework also exist (see e.g., Yakowitz and Parker, 1973;Green and Turner, 1988;Miller et al, 1989). These latter methods also regard a quantized variable as a perturbed copy of the unquantized variable.…”