tfarma_app_gkmu.m

用于模拟时变非平稳的ARMA过程

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)
%   [e-mail] and underlies the GPL.
% 
% MSE-optimal TFARMA system approximation. 

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if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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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));
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end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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alpha= 1/2;

% Dimensions
N= size(Salpha, 1);
LLA= 2*LAR+1;

% Fill the Toeplitz/block-Toeplitz generator rPM
rPM= [];
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 system
AAstack= invert_waxkailath(rPM, RHS);

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if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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rank(toeptoep(rPM))
size(toeptoep(rPM))
Theta= Aml(:);
Theta= Theta(2*LAR+2:end);
rhs= toeptoep(rPM)*Theta

AA= inv(toeptoep(rPM))*RHS
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end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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A= [[zeros(LAR, 1); 1; zeros(LAR, 1)] reshape(AAstack(:, :, end), LLA, MAR)];

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if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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param_norm(A, Aml, 0)
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end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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% The TFMA part
B= 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;

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if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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param_norm(A, Aml, 0)
param_norm(B, Bml, 0)
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end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST
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