qapprox.m 1.68 KB
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 Tilman Steinweg committed Oct 01, 2015 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 % close all clear all % Q-approximation using an improved tau-method (Blanch et al., 1995) % otimization routine: Marquardt-Levenberg global L w Qf1 Qf2 %-------------------------INPUT-PARAMETERS---------------------------- Q0=60.0; % constant Q to be approximated fp1=1.0;fp2=70;df=0.1; % within frequency range fp1,..., fp2 L=3; % number of relaxation mechanisms fl_st=[0.01 0.1 1 5 10 70 200 500 1000 10000]; % L starting values for the relaxation frequencies t=2/Q0; % starting value for tau %-------------------------END: INPUT-PARAMETER----------------------- f=fp1:df:fp2; w=2*pi*f; Qf1=Q0+f*0; % here constant Q-approximation, arbitrary % frequency dependency of Q possible, define % Q as function of frequency here % Qf1=Q0+sin(2*pi*f/fp2)*Q0; % defining option for otimization (see 'help foptions') options(1)=1; options(2)=0.1; options(3)=0.1; options(5)=0; % =0 : Levenberg-Marquardt Method, =1: Gauss-Newton Method options(14)=5000; x=[fl_st t]; % if optimization toolbox is installed use 'leastq' [x,options]=leastsq('qflt',x,options); % output of results: RELAXATIONSFEQUENZ=x(1:L), TAU=x(L+1), sigma=sqrt(sum((Qf2-Qf1).*(Qf2-Qf1))/size(Qf2,2))*100/Q0; GEW_REL_STANDARDABW=sigma, % plot Q as function of frequency: figure('units','normalized','outerposition',[0 0 1 1]) plot(f,Qf1,'b-') hold all plot(f,Qf2,'--'); text(fp2/2,Q0+0.5*(max(Qf2)-Q0),['L=',num2str(L),', Relaxationsfrequenzen: ',num2str(RELAXATIONSFEQUENZ),', Tau=',num2str(TAU),', \sigma=',num2str(sigma)]) xlabel('frequency [hz]'); ylabel('quality factor (Q)'); %axis([fp1 fp2 10 100]);