Optimum lowpass and bandpass filter approximation

摘要

AbstractThe attenuation characteristics of lowpass and bandpass rational filters are approximated by optimizing a weighted error criterion. The analytical approach yields the solution in terms of kernel polynomials, and if the weight function has a particular form, the solution may be given explicitly in terms of the Szegö–Bernstein polynomials; with other weight functions it is necessary to resort to numerical procedures. The solution exhibits a passband behaviour that depends on the chosen weight function; when the Szegö–Bernstein polynomials are used both lowpass and bandpass filters may exhibit equiripple passband attenu