Hi. I would like to know the relationship between the lenght of a signal and its amplitude in frequency domain. I am using a sample code to take the fourier transform of 3 cosine waveforms and recording its amplitudes. However, I have noticed that when I change the length of the signal, the amplitude changes too and I would like to know why. For example, if L = 1000 the amplitudes of the 3 waveforms in frequency domain will be different to the ones when L =2000 and so on.
Thanks in advance! the code that I am using is the following:
Fs = 1000;
T = 1/Fs;
L = 1000;
t = (0:L-1)*T;
x1 = cos(2*pi*100*t);
x2 = 2*cos(2*pi*100*t);
x3 = 4*cos(2*pi*100*t);
X = [x1; x2; x3];
for i = 1:3
subplot(3,1,i)
plot(t(1:100),X(i,1:100))
title(['Row ',num2str(i),' in the Time Domain'])
end
n = 2^nextpow2(L);
dim = 2;
Y = fft(X,n,dim);
P2 = abs(Y/n);
P1 = P2(:,1:n/2+1);
P1(:,2:end-1) = 2*P1(:,2:end-1);
figure(2)
for i=1:3
subplot(3,1,i)
plot(0:(Fs/n):(Fs/2-Fs/n),P1(i,1:n/2))
title(['Row ',num2str(i), ' in the Frequency Domain'])
end
