A WISE method for designing IIR filters

Abstract

Abstract-The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature.

Optimal Design of Magnitude Responses of Rational Infinite Impulse Response Filters

“…Another method is via a WISE approach [19]. An optimal solution can be found by computing a gradient of the corresponding cost function.…”

“…This method is to model rational IIR filters as FIR filters and then minimized the difference between a norm of these two classes of filters. However, since all these methods [4]- [8], [17], [19] are based on formulating their design problems as unconstrained optimization problems, the stability, as well as the size of the ripple magnitudes in passbands and stopbands of the filters, are not guaranteed. Moreover, they required phase information for the desired filter responses.…”

A Procedure for Quasi-Equiripple Linear-Phase IIR Filters Design

“…1) implementation of a phase equalizing allpass filter cascaded with nonlinear-phase IIR filter [1], 2) model-reduction techniques which are applied to approximate the frequency response of finite impulse response (FIR) filter [2], [3], 3) a direct way, i.e., the cost function of the design optimization problem is directly based on desired frequency response [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. In this paper we focus on the latter method.…”

“…The IIR filter design procedures have to guarantee the filter stability which is generally non-easy task. There exist several ways of ensuring the stability of filter resulting from optimization of (1), with good survey of such methods having been presented in [12]. The optimization techniques used for stable IIR filter design can be of either constrained or unconstrained type.…”

A System Identification Based Approach for Design of IIR Digital Filters with Robust Stability

“…The L 2 norm (least squares design [7], [9], [10]) or the L ∞ norm (minimax design [6], [11], [15]) are often employed for the design of digital filters. The L 2 norm criterion optimizes the total quality of digital filter, on the other hand, the L ∞ norm guarantees the lower bound of filter performance.…”