Filter approximation using explicit time and frequency domain specifications
Varun Aggarwal, Wesley O Jin, Una-May O’Reilly · 2006
We demonstrate that particle swarm optimization (PSO) can be successfully used to evolve high performance filter approximations. These evolved approximations use sets of quantitative specifications which conventional analytically derived approximations can not directly employ. The conventional derivations use only a subset of the quantitative specifications in their algorithm and the remaining specifications are side-effect results of the algorithm. Thus, with PSO, instead of a filter designer having access to a limited set of “ specification knobs ” that directly and indirectly achieve performance, a designer has a ”knob ” for each specification that consequently drives the approximation to the desired performance. Categories and Subject Descriptors B.7.2 [Hardware]: Integrated Circuits-Design Aids The primary performance criterion of a filter is its frequency domain magnitude response (henceforth called, magnitude response, defined in Section 3.4). A second set of performance criteria are time domain characteristics. These can be tested by examining the step and impulse responses of the filter. Ideally there should be no oscillations in the step response, a small overshoot in case of oscillations, a low rise time and settling time. A filter meeting the brickwall characteristic has ideal frequency band selection but will oscillate on being activated by a step (in addition to voiding causality). Another criterion is a linear phase response in frequency domain (henceforth called phase response). Finally, because there is a tradeoff between filter complexity (i.e. order) and implementation feasibility, complexity is a performance criterion. 1 0