# i have a signal with many frequencies. how to find this frequencies and reconstruct the signal from these frequencies

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rohith bharadwaj on 10 Aug 2017
Commented: rohith bharadwaj on 29 Aug 2017
I've attached a MATLAB code, in that timeseries is the signal for which frequencies have to be found. I've tried using FFT but not getting the answer. my code for frequency and regeneration: t =0:1:2048; y=timeseries;
ffty = fft(y);
ffty = abs(ffty(1:ceil(length(y)/2))); % ffty(ffty<2)=0; [~,locs] = findpeaks(ffty); freqs = (locs-1)/t(end); signal_1=0; for n=1:1:length(freqs) signal_1 = (signal_1+sin(2*pi*freqs(n)*t)); end hold on plot(smooth(signal_1));
hold on plot(y,'b');

Manan Mishra on 17 Aug 2017
I think this should work for you:
ffty = fft(y);
P2 = abs(ffty/length(ffty));
P1 = P2(1:ceil(length(y)/2));
P1(2:end-1) = 2*P1(2:end-1);
[amp,locs] = findpeaks(P1);
freqs = (locs-1)/t(end);
signal_1=0;
for n=1:length(freqs)
signal_1 = (signal_1+amp(n)*sin(2*pi*freqs(n)*t));
end
hold on;
plot(smooth(signal_1));
plot(y,'b');
Here, P2 is the two-sided spectrum and P1 is the single-sided spectrum.
A two-sided power spectrum displays half the energy at the positive frequency and half the energy at the negative frequency. Therefore, to convert a two-sided spectrum to a single-sided spectrum, you discard the second half of the array and multiply every point except for DC by two.
Also, while regenerating the signal in the "for" loop, you need to take the amplitude of corresponding frequencies into consideration. Hence, you need the first output "amp" of "findpeaks".
You can also eliminate the "for" loop by using vectorization:
signal_1=sum(amp'.*(sin(2*pi*freqs'*t)));
##### 3 CommentsShow 1 older commentHide 1 older comment
Manan Mishra on 18 Aug 2017
You should remove the "smooth" function when plotting as it takes a moving average and averages the different sine signals to zero.
Also, while recreating "signal_1", you should start from the starting point of y and not 0.
Try these changes:
plot(signal_1)
plot(smooth(signal_1));
and
signal_1=y(1);
signal_1=0;
rohith bharadwaj on 29 Aug 2017
thank you. Now I am getting my answer.

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