
Mastering The Fourier Transform in One Day - profquail
http://www.dspdimension.com/admin/dft-a-pied/
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Confusion
You may be able to understand the logic of the FT in one day -- and someone
with a background in math may understand the maths in one day -- but the
problem is usually understanding what the output _means_. With sound the
notion of 'frequency' is reasonably intuitive, but with FT's of other
datasets, the notion of 'frequency' can take a few days to settle in, before
yielding to interpretation.

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yummyfajitas
Typically "frequency" means the same thing: something that is repeated over
time. I'll mention a specific economic example I've seen (sorry, can't recall
exactly where) to illustrate.

Economists wanted to explain a productivity gap between male and female
employees at some employer. So after looking at the Fourier transform of
timeseries of sick days, they noticed that men's sick days behaved like a bump
function near 0. Essentially, if you are sick today, this increases the odds
of him being sick tomorrow.

On the other hand, the Fourier transform of women's sick days had spikes at
f=1/28 days as well as the bump at 0. This means if a woman is sick today, the
odds are increased that she will be sick n x 28 days from now (n an integer).

That's what the Fourier transform does: if your signal has a component which
repeats over time, the Fourier transform will find it.

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cperciva
I would use an autocorrelation for that, not a Fourier transform.

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profquail
"Autocorrelation is essentially the convolution of a function with the same
function reversed in time."

Source:
[http://documents.wolfram.com/applications/signals/Mathematic...](http://documents.wolfram.com/applications/signals/MathematicalUtilities.html)

EDIT: This means that autocorrelation can be calculated using a Fourier
transform, so essentially you'd be using it anyway.

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aswanson
The power-spectral density is the fourier-transform of the autocorrelation of
a time series. So yes, it is the transform dual. But doing the straight
autocorrelation immediately gives you the number of lags before the series
repeats itself and is probably the best way to attack that type of problem.

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jacquesm
The best way to attack that problem is by using common sense, some women have
very heavy periods so it leads to the conclusion that they will periodically
(pun unavoidable) be indisposed.

No heavy math required, said period being 28 days.

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aswanson
Right, for this particular case the math is simply overkill. In the general
case, autocorrelation is a reasonable simple method to determine the
periodicity of a time-series.

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woodson
Quite an interesting read. Another resource I used when I tried to delve into
transforms and DSP was "The Scientist and Engineer's Guide to Digital Signal
Processing" (the whole book is available for free at
<http://www.dspguide.com/>). This was quite helpful, even for me with a
linguistics background.

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anigbrowl
Seconded. Very well written introductory text.

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bbg
... _sinusoid, which is Greek_...

On a pedantic note, sinusoid is at best half Greek. _-oid_ is Greek ("form
of"), but _sinus_ is Latin, referring to, among other things, the fold of a
toga. The English word 'sine', by the way, is rooted in mistranslation from
Arabic:

<http://www.etymonline.com/index.php?term=sine>

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mjtokelly
Numerical Recipes' two chapters on FT (one on implementation, one on
applications) is a longer introduction. It does especially well at addressing
Confusion's point by making FTs' _meaning_ intuitive, across many domains.

<http://www.amazon.com/gp/product/0521880688/>

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mahmud
NR books are gratis online:

<http://www.nrbook.com/a/>

That's the previous "legacy" C version along with Fortran.

The latest version is available as well, behind nasty frames and URLs hidden
in "accept our terms first" javascript _div { display: none; }_ crap.

P.S. I want to be able to write CSS as:

    
    
       typedef div { display: none} hidden_div;     :-D

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4chan4ever
From the comments...

"Can I build a multi effects processor for my electric guitar using a DSP with
the Fourier stuff and the C++ programming?"

"Sure!"

Lol.

