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[TROLLING] From: FFT Analysis for Dummies, From Topic ID: 79806
Woodinville
post Jan 15 2012, 01:26
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QUOTE (Gumboot @ Jan 14 2012, 15:25) *
QUOTE (Woodinville @ Mar 28 2010, 00:00) *
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.



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.


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Gumboot
post Jan 15 2012, 11:25
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QUOTE (Woodinville @ Jan 15 2012, 00:26) *
QUOTE (Gumboot @ Jan 14 2012, 15:25) *
QUOTE (Woodinville @ Mar 28 2010, 00:00) *
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.


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.
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dhromed
post Jan 19 2012, 10:07
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You're quite the eloquent troll. I suggest this thread be partially binned for lowering HA's SNR.
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Gumboot
post Jan 19 2012, 11:42
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QUOTE (dhromed @ Jan 19 2012, 10:07) *
You're quite the eloquent troll.


And yet I'm incapable of expressing one simple point.


QUOTE
I suggest this thread be partially binned for lowering HA's SNR.


Seconded. Kill my account, too.
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