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%  PSD_syn_scale_time_history_wk.m  ver 1.2  Aug 28, 2015
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function[TT,psd_th,dt]=PSD_syn_scale_time_history_wk(psd_th,grms,np,tmax)
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clear TT;
clear new_TT;
clear new_psd_th;
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dt=tmax/(np-1);
TT=linspace(0,(np-1)*dt,np);
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psd_th=detrend(psd_th);
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out5 = sprintf('\n scale time history ');
%% disp(out5)   
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%  scale th
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mu=mean(psd_th);
stddev=std(psd_th);
grmsout = sqrt(mu^2+stddev^2);
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scale=grms/grmsout;
psd_th=psd_th*scale;

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%  Output
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mu=mean(psd_th);
sd=std(psd_th);
mx=max(psd_th);
mi=min(psd_th);
rms=sqrt(sd^2+mu^2);
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n=length(psd_th);
out0 = sprintf(' number of points = %d ',n);
out1 = sprintf(' mean = %8.4g    std = %8.4g    rms = %8.4g \n',mu,sd,rms);
out2 = sprintf(' max  = %9.4g  ',mx);
out3 = sprintf(' min  = %9.4g  \n',mi);
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%% disp(out0);
%% disp(out1);
%% disp(out2);
%% disp(out3);
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%% disp(' ')
%