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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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xnor
post Jan 15 2012, 13:23
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Sorry but the above makes no sense to me, at all.


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Gumboot
post Jan 15 2012, 18:55
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QUOTE (xnor @ Jan 15 2012, 12:23) *
Sorry but the above makes no sense to me, at all.


Yeah, I got that the first time.


QUOTE (SebastianG @ Jan 15 2012, 12:29) *
There's nothing "approximation"-esque about it.


Do you think it would help to repeat it a few more times?
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xnor
post Jan 15 2012, 19:18
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QUOTE (Gumboot @ Jan 15 2012, 19:55) *
Do you think it would help to repeat it a few more times?


Apparently it doesn't seem to help you. :s

This post has been edited by xnor: Jan 15 2012, 19:18


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Gumboot
post Jan 15 2012, 20:39
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Yeah. Fancy that. How could it be that repeating the same thing over and over simply doesn't resolve the issue? It is a mystery.
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Woodinville
post Jan 15 2012, 21:53
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QUOTE (Gumboot @ Jan 15 2012, 11:39) *
Yeah. Fancy that. How could it be that repeating the same thing over and over simply doesn't resolve the issue? It is a mystery.


You seem determined to confuse the FFT with misuses of the FFT.

There is no "approximation" in calculating an FFT (well, beyond numerical resolution).

People may well use the RESULTS to make an approximation. That is a different issue.


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Gumboot
post Jan 16 2012, 09:17
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QUOTE (Woodinville @ Jan 15 2012, 20:53) *
You seem determined to confuse the FFT with misuses of the FFT.


Well, I said nothing of misuse. Approximation is a perfectly legitimate use of any transform and, in fact, I can't think of many uses of the FFT where it isn't acting as an approximation of some other idealised operation which is either not feasible or not adequately characterised.

At issue here is the verb "to be". I marvel at the difficulty some people have with getting their head around that.



QUOTE (saratoga @ Jan 15 2012, 21:11) *
QUOTE (Gumboot @ Jan 15 2012, 05:25) *
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.


This has to be one of the weirdest replies I've seen on HA in a long time. Could you elaborate on what you think this means? Maybe it would help other people to try and understand whatever it is you're getting at.


I seriously doubt it; but I have a few minutes.

I did a shitty job of finding the area of a circle. Why was it shitty? Well, down one path we have "because I was lazy", and down the other we have "the equation was wrong". So why was the equation wrong? Let's look at each operation. The use of a radius is fine. The square is fine. How about the multiply by three? What do we know about three? Three is a fine number, with many irrefutable characteristics. Three is provably three. Three is certainly not an approximation, so the problem must lie elsewhere. Or maybe there is no problem and the answer was correct.

The fact of the matter is that three is an approximation, in this context, of pi. It doesn't matter what else three is. If I use it as an approximation then it is an approximation. Similarly, if someone drives over a river and they don't fall in, they're free to call the structure that kept that from happening a bridge. It's no good to say "it's not a bridge, it's concrete".

And that's probably enough to set people running on a track which is perfectly predictable, but which I don't have time to address right now.
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saratoga
post Jan 17 2012, 00:17
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QUOTE (Gumboot @ Jan 16 2012, 03:17) *
I did a shitty job of finding the area of a circle. Why was it shitty? Well, down one path we have "because I was lazy", and down the other we have "the equation was wrong". So why was the equation wrong? Let's look at each operation. The use of a radius is fine. The square is fine. How about the multiply by three? What do we know about three? Three is a fine number, with many irrefutable characteristics. Three is provably three. Three is certainly not an approximation, so the problem must lie elsewhere. Or maybe there is no problem and the answer was correct.


What I meant is if you could explain what all this stuff about circles has to do with anything. Obviously we all know how to compute the area of a circle. Its the relationship to anything else in this thread that is unclear.

QUOTE (Gumboot @ Jan 16 2012, 03:17) *
And that's probably enough to set people running on a track which is perfectly predictable, but which I don't have time to address right now.


If you can predict that your post would be incomprehensible, aren't you pretty much alone in being responsible? It seems like you want to blame other people here, but its not really their fault if you knowing fail to explain yourself.
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Gumboot
post Jan 18 2012, 06:42
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QUOTE (saratoga @ Jan 17 2012, 00:17) *
What I meant is if you could explain what all this stuff about circles has to do with anything. Obviously we all know how to compute the area of a circle. Its the relationship to anything else in this thread that is unclear.


It's a simpler example.

Evidently not simple enough.



QUOTE (saratoga @ Jan 17 2012, 00:17) *
If you can predict that your post would be incomprehensible, aren't you pretty much alone in being responsible?


I predicted, incorrectly, that having explained one link in a chain of reasoning that gets us closer to the crux of the problem, people would then fumble the next link.

Instead they fumbled at the same place as they started out fumbling.
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saratoga
post Jan 18 2012, 23:48
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QUOTE (Gumboot @ Jan 18 2012, 00:42) *
I predicted, incorrectly, that having explained one link in a chain of reasoning that gets us closer to the crux of the problem, people would then fumble the next link.

Instead they fumbled at the same place as they started out fumbling.


So essentially, the problem was that you underestimated the extent of your own failure to express an idea?
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Gumboot
post Jan 19 2012, 01:00
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QUOTE (saratoga @ Jan 18 2012, 23:48) *
QUOTE (Gumboot @ Jan 18 2012, 00:42) *
I predicted, incorrectly, that having explained one link in a chain of reasoning that gets us closer to the crux of the problem, people would then fumble the next link.

Instead they fumbled at the same place as they started out fumbling.


So essentially, the problem was that you underestimated the extent of your own failure to express an idea?


I couldn't possibly say. I've no idea if anybody read it. Honestly, I doubt anybody did read it.

You could argue that not being read is my own failing, and that perhaps I should have tried to be more engaging by making things more child-friendly, but if I needed to do that then the reality is that I'm probably trying to communicate with people with whom I have no interest in communicating.

From that we can infer that my error was overestimating the value of the participants of this board.

This post has been edited by Gumboot: Jan 19 2012, 01:04
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