[TROLLING] From: FFT Analysis for Dummies, From Topic ID: 79806 
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[TROLLING] From: FFT Analysis for Dummies, From Topic ID: 79806 
Jan 15 2012, 01:26
Post
#1


Group: Members Posts: 1418 Joined: 9January 05 From: In the kitchen Member No.: 18957 
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. No, an FFT is an orthonormal projection, no matter how it's used. It's not the FFT's fault (it has no violition, so how can it be) if somebody uses it in a particular way.  
J. D. (jj) Johnston 


Jan 15 2012, 11:25
Post
#2


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. No, an FFT is an orthonormal projection, no matter how it's used. It's not the FFT's fault (it has no violition, so how can it be) if somebody uses it in a particular way. I don't disagree with that in any way, but the point still stands that the statement is somewhere between vacuous and disingenuous. Similarly, I could calculate the area of a circle by multiplying the square of the radius by three. I could then assert that three is not an approximation because it is the precise midpoint between 2 and 4, and that it is also the sum of 1 and 2, and that it's even itself to the first power. It is precisely what it is. 


Jan 19 2012, 10:07
Post
#3


Group: Members Posts: 1348 Joined: 16February 08 From: NL Member No.: 51347 
You're quite the eloquent troll. I suggest this thread be partially binned for lowering HA's SNR.



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