A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design

Abstract

It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of an FIR filter, the weighted least squares solution is equiripple. The crux of the problem in the design of equiripple filters using the weighted least squares technique lies in the determination of the necessary least squares frequency response weighting function. In this paper, a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. From our experience, it typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response.

Design of stable IIR digital filters with equiripple passbands and peak-constrained least-squares stopbands

“…In a recent paper by Lang [18], Rouché's theorem on the number of zeros of two analytic functions was employed to deduce a stability constraint, which appears to be less conservative than (10).…”

“…The stability of is guaranteed if for (10) where is a lower bound to ensure a reasonable stability margin [20]. In practice, a discrete version of (10) is implemented, i.e., for .…”

Digital filtering of band-limited signals using Periodic Nonuniform Sampling

“…Figure 6 shows that when both implementation schemes, Filter A and Filter B, are realized with ideal filters, they produce identical outputs. Figure 7 shows the magnitude of the spectrum of filtering error when Filter A scheme has been constructed using a lowpass equiripple FIR filter [12] of order 221, which has a transition band of 0.25/T, 0.3 dB passband ripple and -48.99 dB stopband attenuation. Figure 8 shows the magnitude of the spectrum of filtering error when Filter B scheme has been realized, using multiband Chebyshev FIR filters [13] of order 221, with transition band of 0.25/T, 0.3 dB passband ripple and -57.8 dB stopband attenuation.…”

A weighted least squares approach to the design of FIR filters synthesized using the modified frequency response masking structure

“…The least-squares solution of (9) In order to prevent from getting too close to zero, we introduce a lower bound, , similar to the one used in [22] where To accelerate the convergence, is made proportional to a higher power of as given by [22] Here, is the minimax weighting function as indicated before, and is a constant which is selected to maintain a reasonable dynamic range for the value of . As in [22], the constant may be selected as the average value of over all .…”