Need some advice conderning best way to learn FFT and FFT related topics in a timely manner...

Hi all, I am a Phd student in Mechanical Engineering. I have barely ever been introduced to Fourier Transforms and basically never encountered the FFT. Now part of my research requires me to use FFT to get information on data, basically given a set of data I need to be able to extract amplitudes, phases, frequency vectors... and be able to understand them in depth... I have been relying on Google which has given me some insight but I feel like I will not be capable to answer things in depth. I am looking for some opinions on how I can go about learning, books, sites, journals... anything is welcome. Thank you everyone.

Answer 1

[Wayne King]

I wouldn't worry too much about understanding the FFT per se. If you understand the basics of the actual operator, the DFT, you'll know everything you need. The FFT is just an efficient way to code the DFT and there is not just a single FFT algorithm.

Basically any signal processing book will contain ample information on the DFT. Or if you just Google, introduction to the discrete Fourier transform, that should give you a lot of material to read.

[Nina]

Thank you will look into that. My only concern is that my research is purely numerical, I use the Matlab version of the FFT, and I feel like in my thesis defense, i should probably be able to answer questions about the algorithm per say...

[Wayne King]

The actual fft algorithm in MATLAB is built-in (proprietary) so you won't be able to see the code for that, but if you look at this website

FFTW

You should be able to get some good information.

[Matthew Crema]

I feel that Strang's book "Computational Science and Engineering" has a good chapter on the basic concept. And, I would think that your department offers a discrete signal processing course that you should take (or at least "sit in" on the appropriate lectures).

I still expect that Wayne King is correct: your committee will want to make sure you understand the DFT (a linear transform) more than the FFT (a "fast" and well tested algorithm that accomplishes the transform, as I doubt anyone will question at this point).

But you can decide what you might expect upon looking into it further and/or reading Strang's chapter on the DFT, which I recall having a short section on the FFT.

Good Luck!