On Optimal Realizations for All-Pass Fractional Delay Digital Filters

This paper discusses synthesis of optimal realizations with respect to finite wordlength effects for all-pass fractional delay digital filters. In particular this paper focuses on mathematical synthesis of optimal realizations based on state-space representation, and reveals that some well-known realizations such as the balanced realization and the normalized lattice structure provide the optimal realization that simultaneously minimizes the
$L_{1}/L_{2}$
-mixed sensitivity and the
$L_{2}$
-sensitivity. In addition, deviation of frequency responses for the optimal realizations is investigated through some numerical examples.