Enriching the Art of FIR Filter Design via Convex Optimization

The effective design of FIR filters requires judicious compromises to be made between competing properties of the filter. As we have argued herein, when those properties lie in a rich class of design criteria that are convex in the design variables, the inherent tradeoffs between these properties, and filters that attain these tradeoffs, can be reliably obtained. Furthermore, some recently developed software provides a platform that enables these tradeoffs to be obtained with little programming effort. In our examples we only considered pair-wise tradeoffs, but the extension to tradeoff surfaces in higher dimensions is straightforward, even though they tend to be more difficult to visualize. Moreover, the general-purpose convex design platform provides the flexibility to combine convex design criteria in a variety of ways. This platform also offers the opportunity to develop customized algorithms that exploit the structure of particular classes of FIR filter design problems.