function [A, B]= tfarma_app_gkmu(Salpha, MAR, LAR, MMA, LMA, N)% function [A, B]= tfarma_app_gkmu(Salpha, MAR, LAR, MMA, LMA, N)%   This file is part of the TFPM toolbox v1.0 (c)%   michael.jachan@tuwien.ac.at and underlies the GPL.% % MSE-optimal TFARMA system approximation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear;tfpm;N    = 256;MAR  =   5;LAR  =   3;MMA  = MAR-1;LMA  = LAR;re_im= 'i';mo_no= 'n';tfpm_file_gen;%-------------beta = 1/2;alpha= 1/2;Salpha= tfarma_sprf(Aml, Bml, N, alpha);figure(1);tf_show(Salpha)%N= 16;Salpha= (-N/2:N/2-1).'*ones(1, N) + ones(N, 1)*(j*(-N/2:N/2-1));%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%alpha= 1/2;% DimensionsN= size(Salpha, 1);LLA= 2*LAR+1;% Fill the Toeplitz/block-Toeplitz generator rPMrPM= [];for mu= MAR-1:-1:-MAR+1   rPM= [rPM; fliplr(Salpha(N/2-2*LAR+1:N/2+2*LAR+1, N/2+1+MMA+mu).')];end;RHS= [];for m= MMA+1:MMA+MAR   RHS= [RHS; -Salpha(N/2-LAR+1:N/2+LAR+1, N/2+m+1)];end;%[rhs RHS]% Solve the systemAAstack= invert_waxkailath(rPM, RHS);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%rank(toeptoep(rPM))size(toeptoep(rPM))Theta= Aml(:);Theta= Theta(2*LAR+2:end);rhs= toeptoep(rPM)*ThetaAA= inv(toeptoep(rPM))*RHS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%A= [[zeros(LAR, 1); 1; zeros(LAR, 1)] reshape(AAstack(:, :, end), LLA, MAR)];%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%param_norm(A, Aml, 0)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The TFMA partB= zeros(2*LMA+1, MMA+1);for m= 0:MMA   for l= -LMA:LMA      bml= 0;      for mp= 0:MAR         for lp= -LAR:LAR            bml= bml + A(LAR+1+lp, mp+1)*Salpha(N/2+1+l-lp, N/2+1+m-mp);         end;      end;      B(LMA+1+l, 1+m)= bml/N;   end;end;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%param_norm(A, Aml, 0)param_norm(B, Bml, 0)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%