### DFT/FFT

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

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

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?

Owen,

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

Thanks again,

BB

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