Inverse Fourier transform

[@adrianocosta1214]

what if I dont have the original signal in the time domain?
I dont have the fCoefs(fi) to calculate the csw

[@mikexcohen1]

If you don't have the time-domain signal, then you can't compute the FFT. If you already have the Fourier coefficients, you can apply the IFFT to recover the time-domain version.

[@tayyabakhtar6157]

i cant form a graph 3:09 like this , the red color forms a straight line on x-axis

[@mikexcohen1]

Do you mean you don't get circles? That would be "plot(x,y,'ro')". Or do you mean it's a flat line? If you want to send me your code, I can have a look and perhaps help you figure out the problem.
Mike

[@tayyabakhtar6157]

Thank you for your reply ! I had actually copied your code to see the same result but i did'nt get the same output as u r showing here ... it had some errors

[@tayyabakhtar6157]

%% inverse discrete fourier transform
% create the signal
srate = 1000; % hz
time = 0:1/srate:2; % time vector in seconds
pnts = length(time); % number of time points
signal = 2.5 * sin(2*pi*4*time) + 1.5 * sin (2*pi*6.5*time);
% prepare the fourier transform
fourTime = (0:pnts-1)/pnts;
fCoefs = zeros(size(signal));
for fi=1:pnts
% create complex sine wave
csw = exp(-1i*2*pi*(fi-1)*fourTime);
% compute dot product between sine wave and signal
fCoefs(fi) = sum(signal.*csw);
% these are called the fourier coefficients
end
% extract amplitudes
ampls = abs(fCoefs) / pnts;
ampls(2:end) = 2*ampls(2:end);
% compute frequencies vector
hz = linspace(0,srate/2,floor(pnts/2)+1);
figure(1), clf
plot(hz,ampls(1:length(hz)),'s-')
% better:
stem(hz,ampls(1:length(hz)),'ks-','linew',3,'markersize',10,'markerfacecolor','w')
% make plot look a bit nicer
set(gca,'xlim',[0 10],'ylim',[-.01 3])
xlabel('Frequency (Hz)'), ylabel('Amplitude (a.u)')
%% inverse fourier transform
% initialize time-domain reconstruction
reconsignal = zeros(size(signal));
for fi=1;pnts
% create coefficient-modulated complex sine wave
csw = fCoefs(fi) * exp(1i*2*pi*(fi-1)*fourTime);
% sum them together
reconsignal = reconsignal +csw;
end
% divide by N
reconsignal = reconsignal/pnts;
figure(2), clf
plot(time,signal)
hold on
plot(time,real(reconsignal),'ro')
legend({'original';'reconstructed'})
xlabel('Time (s)')
%% one frequency at a time
clear
% set parametres
srate = 1000;
time = 0:1/srate:3;
pnts = length(time);
% create multispectral signal
signal = (1+sin(2*pi*12*time)) .* cos(sin(2*pi*25*time)+time);
% prepare the fourier transform
fourTime = (0:pnts-1)/pnts;
fCoefs = zeros(size(signal));
% here is the fourier transform
for fi=1;pnts
csw = exp(-1i*2*pi*(fi-1)*fourTime);
fCoefs(fi) = sum(signal.*csw)/pnts;
end
% frequencies in hz
hz = linspace(0,srate,pnts);
% setup plotting
figure(3), clf
subplot(211)
plot(time,signal), hold on
sigh = plot(time,signal,'k');
xlabel('Time (s)')
title('Time domain')
subplot(212)
powh = plot(1,'k','linew',2);
set(gca,'xlim',hz([1 end]),'xtick',0:100:900,'xticklabel',[0:100:500 400:-100]);
title('Frequency domain')
xlabel('Frequency (Hz)')
% initialize the reconstructed signal
reconsignal = zeros(size(signal));
% inverse fourier transform here
for fi=1:pnts
% create coeefficients-modulated complex sine wave
csw = fCoefs(fi) * exp(1i*2*pi*(fi-1)*fourTime);
% sum them together
reconsignal = reconsignal + csw;
% update plot for some frequencies
if fi < dsearchn(hz',100) || fi>dsearchn(hz',srate-100)
set(sigh,'YData',real(reconsignal))
set(powh,'XData',hz(1:fi),'YData',2*abs(fCoefs(1:fi)))
pause(.05)
end
end

[@mikexcohen1]

Be careful to use : instead of ; in the for loops -- you were accidentally only looping over an index of 1, not going all the way up to pnts.

[@tayyabakhtar6157]

Thanks it done :) !! thank u very much, ur the best :)

[@HjalmarGuitarMaster]

great video!!

[@niluparupasinghe9499]

Thank you, a great video...

[@luisanarodriguez4037]

Thank you!!!