www.pudn.com > tfarma10.rar > param_tdfk.m, change:2004-01-19,size:3496b

function [TDFKnm, TDFKn0]= param_tdfk(Cnm, Initval) % function [TDFKnm, TDFKn0]= param_tdfk(Cnm, Initval) % This file is part of the TFPM toolbox v1.0 (c) % michael.jachan@tuwien.ac.at and underlies the GPL. % % Computes the Kamen roots [Kamen, LINALG, vol98, pp263, 1988] of % a TV polynomial given through Cnm. If no initial value is % given (Initval==[]), the TDFR with minimum magnitude and phase is % taken?. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear;tfpm; MAR = 0; LAR = 0; MMA = 3; LMA = 2; N = 256; re_im= 'r'; mo_no= 'm'; tfpm_file_gen; %------------- Cml= Bml; Cnm= param_ml_to_nm(Cml, N); %Cnm= ones(N, 1)*BLTI; Initval= []; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Dimensions: NM= size(Cnm); N= NM(1); M= NM(2)-1; % TV Amplification factor TDFKn0= [];% \parc{0}[0:N-1] for n= 0:N-1 cn0= Cnm(n+1, 1);% \parc{0}[n] Cnm(n+1, :)= Cnm(n+1, :)/cn0; TDFKn0= [TDFKn0; cn0]; end; if(nargin==1) Initval= []; end; if(~M)%% Multiplier has no roots! TDFKnm= zeros(N, M);% \PORO{0:0}[0:N-1] else if(M==1)%% Order-1 system has very simple roots! TDFKnm= -Cnm(:, 2);% \PORO{1:1}[0:N-1]= -\parc{1}[0:N-1] else if(isempty(Initval)) % Systen is TI prior to n= 0, takes min-root in abs and angle!! % Initval= sort(roots(Cnm(1, :)));Initval= Initval(end);%*ones(M-1, 1); Initval= j; end; % The recursion if(M>2) PM= Initval*ones(M-1, 1); Enm= []; for n= 0:N-1 eMM= 0; for MM= M-1:-1:1 eMM= [eMM; double(( eMM(M-MM)-Cnm(n+1, 2+MM) )/PM(n+M-MM))]; end; Enm= [Enm; [1; flipud(eMM(2:end))].']; PM= [PM; eMM(M)-Cnm(n+1, 2)]; end; PM= PM(M:end); TDFKnm= [param_tdfk(Enm, Initval) PM]; else%% The final step, M==2 TDFKnm= []; for n= 0:N-1 p1= Cnm(n+1, 3)/Initval; p2= -p1-Cnm(n+1, 2); Initval= p2; TDFKnm= [TDFKnm; [p1 p2]]; end; end;%if(M>2)%% The recursion end; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if(0)% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M= 3; L= 2; Cml= param_rand(M, L, N, 'i', 'n'); Cnm= param_ml_to_nm(Cml, N); Initval= Cnm(N-M+2:N, end) [TDFKnm, TDFKn0]= param_tdfk(Cnm, Initval); figure(1);clf;tfpm_plot_roots(TDFKnm, max(1, max(max(abs(real(TDFKnm))))), ... max(1, max(max(abs(imag(TDFKnm))))), 'x') figure(2);clf;plot(real(TDFKnm8)) mesh(abs(TDFKnm2(N+1:end, :) - TDFKnm8(7*N+1:end, :))) %[TDFKnm2, TDFKn02]= param_tdfk([Cnm;Cnm]); M= 7; L= 5; Cml= param_rand(M, L, N, 'i', 'n'); Cnm= param_ml_to_nm(Cml, N); [TDFKnm81, TDFKn08]= param_tdfk([Cnm;Cnm;Cnm], j*randn); [TDFKnm82, TDFKn08]= param_tdfk([Cnm;Cnm;Cnm], j*randn); figure(1);clf;plot(abs(TDFKnm81)) figure(2);clf;plot(abs(TDFKnm82)) figure(3);clf;plot(abs(TDFKnm82(2*N+1:end, :)-TDFKnm81(2*N+1:end, :))) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end;% TEST TEST TEST TEST TEST TEST TEST TEST TEST TEST %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%