As for the issue with the help example, I am not sure. What are you plotting, abs(fft) or fft^2? That could make the units on the plot look wrong as well. You should probably contact support (link on the right of the blog) and they may have an explanation.

To answer your second question, the normalization of the FFT is arbitrary and many books use different normalizations. It’s just important that the forward and inverse normalizations are paired correctly.

–Loren

The question pertains to line 12 below:
I don’t understand why the fft() function is divided by L and not (2*L).
As a sanity check I tried using this script for a simple DC signal with amplitude 2, Sample rate (Fs) = 102400 Hz,
t = 0:1/Fs:1
%%%%%%
Fs = 102400; t = 0:1/Fs:1; x = 2*ones(length(t),1);
%%%%%%
I expected to see an FFT plot with a peak magnitude of 2 at 0 Hz. Instead it shows a peak of 4. In order to obtain the corresponding time domain amplitude in the frequency domain, I simply modified line 12 to read:

This returns the correct amplitude.

Also out of curiosity, could someone provide some insight as to why this division by the record length was not incorporated into the fft function?

In the recent years open courseware (OCW) has become very popular. Thanks to OCW anyone can freely access pedagogical materials in the form of video lectures from top universities presented by experienced and achieved researchers.

I can recommend the following very useful resources for learning about Fourier transforms (as well as many other topics):

The http://ocw.mit.edu/ and in particular linear algebra lectures by Prof. Gilbert Strang (see lecture 26 for discussion about complex matrices and the fast Fourier transform).

The OCW from Standord University and in particular: the Fourier transform and its applications lectures.

Another popular resource is located at videolectures.net.

Hope this is useful to others, happy learning :)

Kamil

I wrote a little bit about Fourier last year on my blog. Some people have found it useful, and hopefully your readers will too!

http://blinkdagger.com/fourier

Quan