DFT/FFT

Brennon Bortz

Dec 13, 2006, 7:25 PM

Alright. I'm a grad student in music composition and have been learning Max/MSP over the last year. One of the professors that I've been working with has begun to take me back through the basics of digital signal processing, so that I can understand more of the nitty-gritty of what's going on beneaths my Max/MSP experiments.

As would be expected, our studies have brought us upon the DFT and FFT. I am completely stuck and am just not understanding how they work. I can explain very well what takes place when these transforms are used. I guess my issue is that I understand how they work and how they are implemented, but I don't understand the mathematics behind them. I went up through AP Trig/Precalc in high school (10 years ago), but I haven't had any math courses since. I understand a good deal of the math in the DFT/FFT, but if you don't understand it all, you sort oof don't understand any of it...know what I mean?

So, I guess I'm looking for suggestions on how to proceed. My professor "doesn't know how to teach it to me" (his words, not mine), and I am the type of person who desperately wants to understand. Do I need to go to a certain math text(s) to review? Is there a better DFT/FFT introduction out there (so far I've been using Dick Moore's and Miller Puckette's)? What to do?

Thanks for your help,
BB

Brennon Bortz

Dec 13, 2006, 7:47 PM

Sorry, for some reason this post posted twice. Please reply to the other post of the same topic. Moderator, please delete this topic.

Thanks,
BB

Owen Green

Dec 14, 2006, 12:48 AM

To really get to grips with how the (D)FT works, you'll need to
understand calculus and complex numbers. You could probably get a fairly
good grasp of these just on-line. If you haven't done stuff about
Fourier Series yet, do that, and you'll probably need to revise your old
trig along the way.

The best explanation of the DFT I've come across is 'Understanding
Digital Signal Processing' by Richard G. Lyons (Prentice Hall, 2001),
which provides a clear verbal account alongside the maths.

However, it really depends on what it is that you wish to understand how
far you have to drill into the maths. Being able to demonstrate
mathematically, for example, that spectral smearing inevitably occurs in
real life FTs is perfectly possible, IME, without necessarily
understanding why it occurs, and vice versa; that is, it's perfectly
possible to know and understand what's going on without being able to do
the proof at the drop of a hat, or even several hats.

hth,
Owen

Brennon wrote:
> So, I guess I'm looking for suggestions on how to proceed. My
> professor "doesn't know how to teach it to me" (his words, not mine),
> and I am the type of person who desperately wants to understand. Do
> I need to go to a certain math text(s) to review? Is there a better
> DFT/FFT introduction out there (so far I've been using Dick Moore's
> and Miller Puckette's)? What to do?

Brennon Bortz

Jan 21, 2007, 2:54 AM

Owen,

I really appreciate the suggestion. Sorry it's taken me a while to respond!

Thanks again,
BB