program2.m

这是一个优化IIR滤波器的源码,能设计出4个极点0个零点的IIR优化滤波器

(* Code Generated by Mathematica packages written by Brian L. Evans *)
(* Copyright (c) 1993-1997 by the Regents of the University of California *)
(* All Rights Reserved. *)
(* See the copyright file for copyright notice, *)
(* limitation of liability, and disclaimer of warranty provisions. *)
(* Overall Cost Function *)
InputForm[WQ*(-0.5 + Sqrt[(Sqrt[a[1]^2 + b[1]^2]*Sqrt[a[2]^2 + b[2]^2])/
         (a[1]*a[2])]/2) + (Wms*
      integrate[((a[1]^2 + b[1]^2)^2*(a[2]^2 + b[2]^2)^2)/
        (((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))*
          ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))), 
       {w, ws, 100*ws}])/(99*ws) + 
   (Wmp*integrate[(-1 + ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2))/
           Sqrt[((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))*
             ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))])^2, 
       {w, 0, wp}])/wp + (Wmt*integrate[(-(w/(wp - ws)) + ws/(wp - ws) + 
          ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2))/
           Sqrt[((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))*
             ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))])^2, 
       {w, wp, ws}])/(-wp + ws) + 
   (Wph*integrate[(ArcTan[(w - b[1])/a[1]] + ArcTan[(w + b[1])/a[1]] + 
          ArcTan[(w - b[2])/a[2]] + ArcTan[(w + b[2])/a[2]] - 
          (3*w*((-2*wmax*a[1] - 
                  (ArcTan[(wmax - b[1])/a[1]] + 
                     ArcTan[(wmax + b[1])/a[1]])*
                   (-wmax^2 - a[1]^2 + b[1]^2) - 
                  a[1]*b[1]*Log[1 + (wmax - b[1])^2/a[1]^2] + 
                  a[1]*b[1]*Log[1 + (wmax + b[1])^2/a[1]^2])/2 + 
               (-2*wmax*a[2] - 
                  (ArcTan[(wmax - b[2])/a[2]] + 
                     ArcTan[(wmax + b[2])/a[2]])*
                   (-wmax^2 - a[2]^2 + b[2]^2) - 
                  a[2]*b[2]*Log[1 + (wmax - b[2])^2/a[2]^2] + 
                  a[2]*b[2]*Log[1 + (wmax + b[2])^2/a[2]^2])/2))/wmax^3)^2, 
       {w, 0, wmax}])/wmax + 100*WO*
    (-1 + ((a[2]^2 + b[2]^2)*(b[1]*
             Cos[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + 
               ArcTan[(b[1] + b[2])/(a[1] - a[2])]] + 
            a[1]*Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + 
               ArcTan[(b[1] + b[2])/(a[1] - a[2])]])*
          (1 - E^(tpeak1*a[1])*
             (Cos[tpeak1*b[1]] - 
               ((a[1] - ((a[1]^2 + b[1]^2)*
                       Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + 
                         ArcTan[(b[1] + b[2])/(a[1] - a[2])]])/
                     (b[1]*Cos[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + 
                         ArcTan[(b[1] + b[2])/(a[1] - a[2])]] + 
                       a[1]*Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + 
                         ArcTan[(b[1] + b[2])/(a[1] - a[2])]]))*
                  Sin[tpeak1*b[1]])/b[1])))/
        (b[1]*Sqrt[((a[1] - a[2])^2 + (b[1] - b[2])^2)*
            ((a[1] - a[2])^2 + (b[1] + b[2])^2)]) + 
       ((a[1]^2 + b[1]^2)*(b[2]*
             Cos[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + 
               ArcTan[(b[1] + b[2])/(-a[1] + a[2])]] + 
            a[2]*Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + 
               ArcTan[(b[1] + b[2])/(-a[1] + a[2])]])*
          (1 - E^(tpeak1*a[2])*
             (Cos[tpeak1*b[2]] - 
               ((a[2] - ((a[2]^2 + b[2]^2)*
                       Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + 
                         ArcTan[(b[1] + b[2])/(-a[1] + a[2])]])/
                     (b[2]*Cos[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + 
                         ArcTan[(b[1] + b[2])/(-a[1] + a[2])]] + 
                       a[2]*Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + 
                         ArcTan[(b[1] + b[2])/(-a[1] + a[2])]]))*
                  Sin[tpeak1*b[2]])/b[2])))/
        (b[2]*Sqrt[((-a[1] + a[2])^2 + (-b[1] + b[2])^2)*
            ((-a[1] + a[2])^2 + (b[1] + b[2])^2)]))^2]
(* Derivatives have been omitted *)