FFT Analysis for Dummies Options

[Ethan Winer]

Folks,

I'd like to learn more about FFTs. I'm not a math guy, so I imagine I'll never fully understand all the nuances. But I'd like to try anyway. I understand the general concept, that an FFT shows how much energy is present at different frequencies. What I'd like to know is how to set the various parameters such as FFT Size and Overlap, when to use the different types of window smoothing and why, and so forth. Below is a list of settings in the Rightmark FFT analyzer with my associated questions, and hopefully this is a good place to start.

FFT Size: I understand that the higher the number, the better the frequency resolution. So why is this
even adjustable? Why not just use the highest resolution possible automatically?

Zero Padding: This ranges from None through 8x. What does this do?

FFT Overlap: What is this for, and when would you use higher or lower values?

FFT Window: I recognize some of the names, but have no idea when or why one would select these choices.

Kaiser Window beta: I have no idea what this does either.

I noticed that Sound Forge lets you pick the number of slices to show. What are slices and why is more than
one needed to analyze a Wave file?

I realize this is a lot to ask! If anyone knows of a good newbie-level tutorial that explains this in plain English with minimal math, I'd love to see it. Everything I've found through Google starts right in with math that's way over my head.

--Ethan

[Woodinville]

Ok.

An FFT is a discrete-time, finite length linear algebraic transform. It is orthonormal, which is to say it is a tight frame, or 1 to 1 and onto.

It uses a set of basis vectors that are derived directly from the complex exponential used in the continuous-time, continuous-frequency Fourier Transform.

As a result of the periodic nature of the FFT basis vectors, it is periodic across block boundaries, i.e. it looks like the data repeats to infinity, if you are doing a 2-point fft on two values, say 1 and -1 (yes, that's ridiculous, but it makes the point), the result is the same as calculating the full integral form on the infinite sequence 1 -1 1 -1 1 -1 1 -1 1 -1 ....

Among other things, this means that for signals that are not periodic at a block length, there will be a discontinuity at the ends.

This is why you do windowing, it removes the discontinuity at the ends of the block by windowing the signal to zero.

A window is nothing but the impulse response of a lowpass filter with specific properties.

I have to go shopping. So more later?

Some points, an FFT is not an approximation, nor is it a model. It is a precise transform with a precise inverse, one that obeys power and amplitude conservation both in the time and short-term frequency domain. In this it is actually marginally more precise than the full Fourier Transform, which suffers some zero-power, small amplitude issues, but that only with signals that can not exist in the real world, perhaps outside of astrophysics.

Must go, spouse grumbling.

[Gumboot]

Some points, an FFT is not an approximation, nor is it a model. It is a precise transform with a precise inverse, one that obeys power and amplitude conservation both in the time and short-term frequency domain.

I take exception to this. An FFT, like anything else, is a model and/or an approximation if it is used as such. Sometimes 3 is an approximation of pi. There's no fantastic mathematical property that can stop something from being used as a very blunt instrument.