FFT Analysis for Dummies 
FFT Analysis for Dummies 
Mar 27 2010, 21:41
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#1


Group: Members Posts: 248 Joined: 12May 09 From: New Milford, CT Member No.: 69730 
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 I realize this is a lot to ask! If anyone knows of a good newbielevel 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  I believe in Truth, Justice, and the Scientific Method



Mar 28 2010, 01:00
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#2


Group: Members Posts: 1402 Joined: 9January 05 From: JJ's office. Member No.: 18957 
Ok.
An FFT is a discretetime, 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 continuoustime, continuousfrequency 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 2point 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 shortterm frequency domain. In this it is actually marginally more precise than the full Fourier Transform, which suffers some zeropower, small amplitude issues, but that only with signals that can not exist in the real world, perhaps outside of astrophysics. Must go, spouse grumbling.  
J. D. (jj) Johnston 


Jan 15 2012, 00:25
Post
#3


Group: Members Posts: 51 Joined: 11December 11 From: United Kingdom Member No.: 95728 
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 shortterm 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. 


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