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  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
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.

  • xnor
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  • Developer
[TROLLING] From: FFT Analysis for Dummies
Reply #1
Sorry but the above makes no sense to me, at all.
"I hear it when I see it."

  • SebastianG
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  • Developer
[TROLLING] From: FFT Analysis for Dummies
Reply #2
I don't disagree with that in any way, but the point still stands that the statement is somewhere between vacuous and disingenuous.

The point doesn't stand at all. The DFT is just that, an
- invertable
- discrete
- linear
mapping with some other nice properties. There's nothing "approximation"-esque about it.

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #3
Sorry but the above makes no sense to me, at all.


Yeah, I got that the first time.


There's nothing "approximation"-esque about it.


Do you think it would help to repeat it a few more times?

  • xnor
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  • Developer
[TROLLING] From: FFT Analysis for Dummies
Reply #4
Do you think it would help to repeat it a few more times?


Apparently it doesn't seem to help you. :s
  • Last Edit: 15 January, 2012, 01:18:44 PM by xnor
"I hear it when I see it."

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #5
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.

  • Woodinville
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[TROLLING] From: FFT Analysis for Dummies
Reply #6
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.
-----
J. D. (jj) Johnston

  • saratoga
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[TROLLING] From: FFT Analysis for Dummies
Reply #7
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.

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #8
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.



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.

  • SebastianG
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  • Developer
[TROLLING] From: FFT Analysis for Dummies
Reply #9

There's nothing "approximation"-esque about it.

Do you think it would help to repeat it a few more times?

As long as you appear to make little sense and don't seem to understand what people are telling you, repetition and rewording is among the few options that could help, yes.

Quote from: Gumboot link=msg=0 date=
[...]
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.

It's acting always the same. It turns N complex samples into other N complex samples in a linear and invertable way. But I guess, when you hear "FFT" you're thinking of more than just the FFT. You're thinking of spectral analysis. Many collegues of mine also don't make this distinction. When they say "do an FFT on that signal" they really mean "divide your signal into overlapping blocks, window them, perform an FFT per each block, take the absolute value squared and average them to approximate the power spectral density" (Welch's method). That's pretty much the difference between an engineer and a mathematician.

Example1: performing a fast convolution using the FFT has nothing to do with approximations.
Example2: using the FFT to compute the type-IV DCT efficiently has nothing to do with approximations.

Cheers!
SG
  • Last Edit: 16 January, 2012, 05:28:39 AM by SebastianG

  • knutinh
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[TROLLING] From: FFT Analysis for Dummies
Reply #10
Example1: performing a fast convolution using the FFT has nothing to do with approximations.
Example2: using the FFT to compute the type-IV DCT efficiently has nothing to do with approximations.

Multiplying 2 really large numbers seems to be in the same cathegory:
http://en.wikipedia.org/wiki/Multiplicatio...ansform_methods

  • Woodinville
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[TROLLING] From: FFT Analysis for Dummies
Reply #11
Find the approximation:

clear all
close all
fclose all

len=2^12;
fs=44100;

wind=hann(len); # make the hann window
slen=len/2; # the shift length, i.e. 1/2 overlap.

x=wavread('01jt.wav');  # or you can specify any other wave file, of course.
whos  # shows the form of the file, n samples by 2 channels

flen=length(x); # gets the length of the file in samples

nblk=floor(flen*2/len)-1 # might clip the end of the file
nonzeroblocks=0;

lenspec=len/2+1; # length of the spectrum
sumspec(1:lenspec,1:2)=0; # to keep overall power spectrum

for ii = 1:1:nblk
   work=x( ((ii-1)*slen +1): ((ii+1)*slen) , 1:2); # pick one block of data
   work(1:len,1)=work(1:len,1) .* wind;  # window left channel
   work(1:len,2)=work(1:len,2) .* wind;  # ditto right channel
   ss=sum(sum(abs(work)))  # is there any energy here?
   if ss > 1/32768  # if it's smaller than that there is no signal.
      nonzeroblocks=nonzeroblocks+1;
      workt=fft(work); # take the transform
      ps=workt(1:lenspec,1:2) .* conj(workt(1:lenspec,1:2));
      sumspec=sumspec + ps; # keep overall power spec sum.
      psmax=max(max(ps)); # find overall maximum
      ps=ps/psmax; #normalize to peak for presentation
      ps=max(ps,.00000000001); # put in minimum energy to avoid stuff
      ps=log10(ps)*10; # dB spectrum.
      subplot(2,1,1);
      plot(work);
      subplot(2,1,2)
      plot(ps);

   end

   fflush(stdout);  # this slows things down but makes sure
          # we see the output from the program
   junk=input('hit cr');

end
  • Last Edit: 16 January, 2012, 06:30:41 PM by Woodinville
-----
J. D. (jj) Johnston

  • saratoga
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[TROLLING] From: FFT Analysis for Dummies
Reply #12
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. 

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.

  • Woodinville
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[TROLLING] From: FFT Analysis for Dummies
Reply #13
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".


Whatever are you on about?

An FFT is a precise, orthonormal projection.  There is no approximation. It is what it is.
-----
J. D. (jj) Johnston

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #14
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. 



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.

  • knutinh
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[TROLLING] From: FFT Analysis for Dummies
Reply #15
Instead they fumbled at the same place as they started out fumbling.

I am sorry, but the logic of internet discussion is that if you are unable to explain your thoughts clearly initially, then don't care about explaining what you really meant, the world will respond with a big yawn.

-k

  • saratoga
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[TROLLING] From: FFT Analysis for Dummies
Reply #16
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?

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #17
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.
  • Last Edit: 18 January, 2012, 07:04:03 PM by Gumboot

  • Gumboot
  • [*][*]
[TROLLING] From: FFT Analysis for Dummies
Reply #18
[...] then don't care about explaining what you really meant, [...]


Now that isn't what I said, is it.  What did I say?  Can you repeat it back to me in your own words?

  • tpijag
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[TROLLING] From: FFT Analysis for Dummies
Reply #19
Would you consider increasing your content to pointless antagonism ratio? There is no prize for being ill-mannered.

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #20
Would you consider increasing your content to pointless antagonism ratio? There is no prize for being ill-mannered.


And by "content" do you mean repetition?

What I said I said in plain English.  It didn't work, so I gave another example of what I was talking about.  That didn't work, so I pointed directly at the verb that I disputed.  That didn't work, either.

Throughout there's been a continuous paraphrasing of scenes from This is Spinal Tap and Idiocracy, and speculation on my capability to express something which is exceedingly trivial.

I see similarly stupid exchanges on this board in other threads, including those in which I'm not involved.  For all I know it's some kind of trial-by-dipshit hazing ritual to see how newbies keep it together under the strain of abject stupidity.

So far I'm just going along with it to see where it leads, but you can hardly expect me to take this seriously, can you?

  • dhromed
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[TROLLING] From: FFT Analysis for Dummies
Reply #21
You're quite the eloquent troll. I suggest this thread be partially binned for lowering HA's SNR.

  • Gumboot
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[TROLLING] From: FFT Analysis for Dummies
Reply #22
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.

  • derty2
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[TROLLING] From: FFT Analysis for Dummies
Reply #23
I never thought I would ever come across a thread named ("FFT Analysis for Dummies" AND "dummy spitting").