在MATLAB中用FFT重构时间序列

Question

我正在尝试重建来自FFT的太阳黑子信号，时间序列和周期图位于以下站点http://www.mathworks.com/help/matlab/examples/using-fft.html。我编写了以下代码，但结果与原始wave不同：

YY=Y(1:floor(n/2))
% magnitude 
mag_fft = 2*abs(YY)/length(Y);
% phase angle
ang_fft = angle(YY);


[new_mag,new_i]=sort(mag_fft,'descend');
new_ang=ang_fft(new_i);
new_freq=freq(new_i)
wave=zeros(1,length(YY));
wave=new_mag(1);
t=1:length(YY)

for(i=1:70)
wave=wave+new_mag(i).*sin(2*pi*new_freq(i)*t+new_ang(i));
end 
wave=wave-mag_fft(1)
figure;plot(year(t),wave,'-b')
hold on;plot(year(t),relNums(t),'-r')

任何想法？

Answer 1

%http://www.mathworks.com/help/matlab/examples/using-fft.html
% sunspots 
% sunspots have period of 10 years
%% 
clc;clear all;close all;
load sunspot.dat
 year=sunspot(:,1);
relNums=sunspot(:,2);
figure;plot(year,relNums)
title('Sunspot Data')
 plot(year(1:50),relNums(1:50),'b.-');

 yfft = fft(relNums);%figure;plot(ifft(yfft)-data1d,'r')
 %yfft = fft(data1d);   iyfft=ifft(yfft);
 [sum(relNums)  yfft(1)]
 yfft(1)=[];  % we grid rid of the first value as it corresponeding to   zero frequency.
 N=length(yfft)+1;
 yfft=yfft.*2./N;
 %%
 power_fft = abs(yfft);power1_fft = sqrt(yfft.*conj(yfft));
 figure;plot(power_fft,'-b');hold on;plot(power_fft,'rO')

 ang_fft = angle(yfft);real_fft= real(yfft);imag_fft= imag(yfft);
 figure;plot(real_fft);hold on;plot(imag_fft,'-r')
 figure;plot(angle(yfft))
  ph = (180/pi)*unwrap(ang_fft); % phase in degrees

 % Now the total length of the per and all other powers should be N-1 because there is no
 % more corresponding poweres and phases, and the number of frequencies before the nequiest is 
   Nneq=length(N./(1:N/2));

    Nm1=N-1;  per=N./(1:Nm1);   freq=1./per;
  [per'/12   power_fft(1:Nm1)/100 ] % so as to display the period in years

  %% ytyt
  ndat=length(relNums);
  x=0:ndat-1;
  sumharmony1(1:Nneq,1:ndat)=0;
  sumharmony2(1:Nneq,1:ndat)=0;

  for i=1:Nneq
   % those two forms are equal, the last one is called the cos form.
    %     sumharmony1(i,:)=sumharmony1(i,:)+real_fft(i)*cos(2*pi*x/(per(i)))-   imag_fft(i)*sin(2*pi*x/(per(i)));
    sumharmony1(i,:)=sumharmony1(i,:)+power_fft(i)*cos(2*pi*x./(per(i))+ang_fft(i));

  end
   y1 =sum(relNums)/N+ sum(sumharmony1);
   %y2 =sum(tmp)/N+ sum(sumharmony2);

  figure;plot(relNums);hold on; plot( y1, 'r');
 figure;plot((relNums-y1')) % However, the excellent results, we couldnot yet reach to the that of the built in function ifft.
  figure;plot(relNums(1:100),'-ob');hold on; plot( y1(1:100), 'r');
   % note that we multiply by 2 because of using the window hanning.enter code here