# Matlab FFT-algorithm example, one simple question

This is a question about an example for the software Matlab, but I still chose to ask it here, since I suspect that the question is more about the math involved than the software itself.

I want to use Matlab's Fast Fourier Transform (FFT) algorithm to find out how the frequencies are distributed in a soundsample. However, there is one thing that is bugging me in the example Mathworks has on their website over here. It's probably really obvious, but I just can't seem to understand why they are doing this one thing.

In the example they first create a sample of two sinusoidal waves together with simple white noise. Then they try to extract to frequencies of these two waves from the sample with the help of the FFT-algorithm:

1    NFFT = 2^nextpow2(L);     % Next power of 2 from length of y
2    Y = fft(y,NFFT)/L;
3    f = Fs/2*linspace(0,1,NFFT/2+1);
4        % Plot single-sided amplitude spectrum.
5    plot(f,2*abs(Y(1:NFFT/2+1)))
6    title('Single-Sided Amplitude Spectrum of y(t)')
7    xlabel('Frequency (Hz)')
8    ylabel('|Y(f)|')


Now, here is what I don't understand. On line 2 they divide the the transform by L, the amount of samples used, to get Cn, the amplitude of the wave e^inx, right? Then why do they need to multiply this amplitude by 2 on line 5 before they can get the original amplitudes of the two waves.

• @Laph: why would they have had to do that? The plot would have looked the same regardless, save for the ticks on the ordinate. You are right: the spectrum has little value after $512$ Hz because they zero-padded to get the power of two they supposedly needed (although I thought this was no longer needed after the FFTW algorithm gained prominence). – Ron Gordon Feb 10 '13 at 17:02