doubt fft with values

If you see, there is sin( 2 pi 15* t) signal and I want to show the spectrum of it. The problem what I see it's that there are 2 impulses, ones on 15 Hz (it's right) but other on 35 Hz. And the other problem it's that the signal magnitude is approximately 200 but the signal has an amplitud of 1.

Answer 1

[Julian Oviedo]

Thanks. I work!, but I do not understand why I should divide the fft(x)'s vector by lenght(x).

For example in the next picture, the max lobule must to be on 100 Hz. why not is there?

Answer 2

[Star Strider]

If you want to plot a two-sided Fourier transform, you need to define your frequency vector differently and use the fftshift function:

t = 0 : 1/50 : 10-1/50;
x = sin(2*pi*15*t);

y = fft(x)/length(x);
m = abs(y);
a = angle(y);
f = -25: 1/10 : 25-1/10;

figure(1)
subplot(2,1,1)
plot(f, fftshift(m))
grid
subplot(2,1,2)
plot(f,a)
grid

figure(2)
plot(t, x)
grid
axis([0  1    -1  1])

To plot a one-sided Fourier transform, see the R2015a documentation for the fft (link) specifically the code between the first (top) two plot figures.

[Star Strider]

Julian Oviedo’s ‘Answer’ moved here:

why do you do y = fft(x)/length(x);

it's because the library fft or what?

Sorry for be insistent but I need to know to work in the future with this

[Star Strider]

The fft as calculated does not normalise by the energy in the signal, so it is necessary to do that in your code by dividing by the length of the original signal. See the documentation for fft and textbook discussions of the fast Fourier transform. The fft code does not do this because it is common to zero-pad the original signal to increase the frequency resolution, increase the computational efficiency of the fft calculation, or both. The fft code ‘sees’ only the signal that you give it, not the original signal without the zero-padding. Zero-padding adds no energy to the signal, so dividing the Fourier-transformed signal by the length of the padded signal would give an erroneous result.

If my Answer solved your problem, I would have hoped for you to Accept it.