Semi-infinite linear programming: a unified approach to digital filter design with time- and frequency-domain specifications

Using the recently developed semi-infinite linear programming techniques and Caratheodory´s dimensionality theory, we present a unified approach to digital filter design with time and/or frequency-domain specifications. Through systematic analysis and detailed numerical design examples, we demonstrate that the proposed approach exhibits several salient features compared to traditional methods: 1) using the unified approach, complex responses can be handled conveniently without resorting to discretization; 2) time domain constraints can be included easily; and 3) any filter structure, recursive or nonrecursive, can be employed, provided that the frequency response can be represented by a finite-complex basis. More importantly, the solution procedure is based on the numerically efficient simplex extension algorithms. As numerical examples, a discrete-time Laguerre network is used in a frequency-domain design with additional group-delay specifications, and in a ℋ_∞-optimal envelope constrained-filter design problem. Finally, a finite impulse response phase equalizer is designed with additional frequency domain ℋ_∞ robustness constraints