Comments on: The DFT “à Pied”: Mastering The Fourier Transform in One Day

By: Daniel P

Daniel P — Tue, 29 Apr 2008 12:16:38 +0000

I have an approximately sinusoidal signal, x, and I have calculated the abs(FFT(x)) with Matlab. My question is, what is the meaning of the magnitude I obtain? Does this magnitude have any relation to the input signal amplitude? To the number of bins? To the main frequency? Am very confused as to the meaning of FFT magnitudes and cannot find anywhere, please HELP!

By: Bernsee

Bernsee — Wed, 23 Apr 2008 06:39:11 +0000

If you’re referring to the phase information that you can obtain from the transform, the reference for the bin phase is the first sample of the time domain sequence.

By: Arun Aiyer

Arun Aiyer — Tue, 22 Apr 2008 22:24:12 +0000

When phase is calculated from PSD curve, what is the reference point for the computed phase?

By: Bernsee

Bernsee — Sun, 20 Apr 2008 08:35:54 +0000

In a nutshell and without delving too deep into the maths - we know (from the article) that we need transformLength bins (sine waves) in order to fully represent the signal, this is why we loop through the bins from 0 to transformLength-1. When we’re done with that, each of the bins holds a coefficient that defines how much the input signal “looks like” a sine wave at that bin frequency (bin frequency is calculated as arg). In order to ‘compare’ the sine wave with our signal we multiply the input signal (which is stored in inputData[0] through inputData[transformLength-1]) with a sine wave of the same length at the frequency of interest and add the results to the bin coefficient. You could see this as a filtering or correlation operation between the sine wave and our signal. Clearly, if the sine wave at that frequency looks very much like our input signal that coefficient will be large. If the signal doesn’t contain this frequency our coefficient at that bin will be zero, or very small.

Hope this helps!
–smb

By: Mike

Mike — Sat, 19 Apr 2008 14:22:09 +0000

Well for instance, if we look at the listing 1.1, it’s not clear to me why the bins are computated that way. I dont like to just copy/paste formulas. I like to understand them, in and out.
My programming background is good, however i cannot say the same about my maths or even DSP.
Maybe the books that you have mentionned in your FAQ will help me get started?

Thanx.

By: Bernsee

Bernsee — Sat, 19 Apr 2008 06:09:28 +0000

What is it exactly that you didn’t understand? I’d be happy to clarify if you would let me know what the problem is.

By: Mike

Mike — Fri, 18 Apr 2008 20:51:56 +0000

This article was clear till the first code listing…

By: Shaurya Malhotra

Shaurya Malhotra — Sun, 16 Mar 2008 14:12:46 +0000

I wish I had found this page (and this website) earlier!! Very well explained.
I also saw found many other interesting articles on this site. Will read them too.
Thanks a lot..

By: Bernsee

Bernsee — Fri, 07 Mar 2008 06:15:37 +0000

Thank you, I’m glad you like it!

By: Dave

Dave — Sun, 02 Mar 2008 22:55:53 +0000

I gotcha now. This is the best from zero to sixty article on DFT/FFT anywhere on the web. Thanks so much for putting it together!