Using the recently developed semi-infinite linear programmingntechniques and Caratheodory's dimensionality theory, we present anunified approach to digital filter design with time and/ornfrequency-domain specifications. Through systematic analysis andndetailed numerical design examples, we demonstrate that the proposednapproach exhibits several salient features compared to traditionalnmethods: 1) using the unified approach, complex responses can be handlednconveniently without resorting to discretization; 2) time domainnconstraints can be included easily; and 3) any filter structure,nrecursive or nonrecursive, can be employed, provided that the frequencynresponse can be represented by a finite-complex basis. More importantly,nthe solution procedure is based on the numerically efficient simplexnextension algorithms. As numerical examples, a discrete-time Laguerrennetwork is used in a frequency-domain design with additional group-delaynspecifications, and in a ℋ∞-optimal envelopenconstrained-filter design problem. Finally, a finite impulse responsenphase equalizer is designed with additional frequency domainnℋ∞ robustness constraints
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