FFT does not return the amplitudes in matlab?

Question

I have generated the following time signal: enter image description here

Now I want to perform a Discrete Fourier Transform by using the matlab command fft

Here is my code:

function [ xdft, omega ] = FastFourier( t, fs )

%% Inputs from other functions %%
[P_mean, x, u] = MyWay( t )   %From here comes my signal x(t)

%% FFT %%
xdft1 = fft(x);                  % Perform FFT
xdft2 = abs(xdft1);              % Take the absolute value of the fft results
xdft = xdft2(1:length(x)/2+1);   % FFT is symmetric, second half is not needed
freq = 0:fs/length(x):fs/2;      % frequency axis

plot (freq(1:100),xdft(1:100));

end

And here is the plot that I get: enter image description here

And what is puzzling to me is the y axis? Shouldn't the y axis represent the amplitudes of the frequency components? Is there a way to get the amplitudes of all the frequency components?

Thanks!

EDIT: I have found that some people do the following:

n = size(x,2)/2;      %The number of components and second half can be neglected again
xdft2 = abs(xdft1)/n;

This way I seem to get the amplitude spectrum, but why do I have to divide the absolute value by n?

Additional answer may be found at the related question (dsp.stackexchange.com/questions/14636/…) — Lutz Lehmann

ben ben · Accepted Answer · 2014-02-25T08:52:08

FFT gives you a complex pair in each Frequency Bin. The first bin in the FFT is like the DC part of your signal (around 0 Hz), the second bin is Fs / N, where Fs is the sample rate and Nis the windowsize of the FFT, next bin is 2 * Fs / N and so on. What you calc with the abs() of such a pair is the power contained in a bin.

you might also want to check this out: Understanding Matlab FFT example

FFT does not return the amplitudes in matlab?

3 Answers