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 an d Caratheodory's dimensionality theory, we present a unified approach to di gital filter design with time and/or frequency-domain specifications. Throu gh systematic analysis and detailed numerical design examples, we demonstra te 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 p rocedure is based on the numerically efficient simplex extension algorithms . As numerical examples, a discrete-time Laguerre network is used in a freq uency-domain design with additional group-delay specifications, and in a H- infinity-optimal envelope constrained filter design problem. Finally, a fin ite impulse response phase equalizer is designed with additional frequency domain H-infinity, robustness constraints.