MATLAB: How to separate signals with diffrent frequencies

fftwavelet

t = linspace(0, 1, 1001);
x=sin(2*pi*t*3) + sin(2*pi*t*6) + sin(2*pi*t*10)+sin(2*pi*t*13)+sin(2*pi*t*20)+sin(2*pi*t*50)+sin(2*pi*t*100)+sin(2*pi*t*200);
% my signal with frequencies 3,6,10,13,20,50,100,200 KHz
sigma=0.1;
y=x+randn(size(x)).*sigma; % adding noise
I filtered the signal using fft.
I want to separate signals.
Eg : from my original signal, I want a signal with frequency range say 3 to 8 KHz, another signal say from 100 to 200 KHz. How can I separate them and display those signals.How can I do this. Anybody Please help me to solve this.?

Best Answer

Add the following lines of code at the bottom of your code (after y=x+randn(size(x)).*sigma;):
ffty = fft(y);
ffty = abs(ffty(1:ceil(length(y)/2)));
ffty(ffty<100)=0;
[~,locs] = findpeaks(ffty);
freqs = (locs-1)/t(end)
signal_1 = sin(2*pi*t*freqs(1))+sin(2*pi*t*freqs(2))+sin(2*pi*t*freqs(3)); % 3-10
signal_2 = sin(2*pi*t*freqs(6))+sin(2*pi*t*freqs(7)); % 50-100
subplot(211), plot(t,signal_1)
subplot(212), plot(t,signal_2)
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