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Fourier Analysis
Name: James
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: N/A
Question:
Hello. I am in need of a low-level course that teaches
Fourier analysis. I have read "Who is Fourier: A Mathematical
Adventure" which was very helpful because it did not bury me in
mathematics that I did not understand. It was primarily conceptual.
I have searched my university library but wa unable to find anything
that was not far above my mathematical abilities.
I have attained a fairly poor level of mathematics--only going as
far as understanding a limit and simple integration/differentiation.
Because this is all new to me I am unaware of what specific form
of Fourier analysis will suit my needs. I'm certain that Fourier
analysis is a major field of study in its own right, so I feel rather
uneasy about what to ask for. I am examining the pattern of force
depressions from a rats tongue as it licks a tube for milk over a
30-minute period. Apart from putting the data in SigmaPlot for
Windows and calculating a power spectrum, I don't know what else
to do with the data. I feel certain there are a world of opportunites
out there. Thank you for your help.
Replies:
It seems like you are basically looking at your rat-tongue data and trying
to "analyze it". And one method to do so you think would be fourier
analysis.
Maybe you'll learn more about what you need to learn, as you plug along with
this. But the concepts with fourier analysis are reasonably straight
forward, but I just worry that it is still hard to get by the "so what?"
question. This is not to say negative things about your approach, its just
that understanding real life is never easy.
You can understand that you can look at a movement which seems complex and
perhaps break it down into the sum over lots of simpler movements. Fouirier
analysis lets you break down a complex curve into the sum of many sine waves
of different amplitudes, different phases, different frequencies. A person
can talk about this alot, but then comes the so what question.
Perhaps you don't know what you are looking for and then maybe the fourier
analysis with just help you push along. You would not be the only person in
the "what am I doing" catagory! There are those Schaum's outline series in
math, one on Fourier analysis. Very no-nonsense, lots of examples and
sample problems.
Fourier analysis tho in the end is cook-book. You put your numbers into this
"machine" and it computes things like that pwr spectral density. THere is not
necessarily any more that it can do. I'm sure you can learn the mechanics of
how to use this cook-book machine, but few people memorize it for long
periods of time.
You can have some fun with all this with your math packages for your
computer. Add up various combinations of sine waves and just see the result
emerging. For example sin x - 1/3 sin3x + 1/5 sin 5x etc etc, add it up, I
think it gives a square wave. So in your mind you can visualize that it is
possible to go back the other way, given the square wave, how can you break
it into its simpler parts, well you do this fourier analysis stuff. At least
now this is the concept.
Sort of a vague answer I know. Good luck. There is something to what you
are doing, but it is not something so simple that I (anyway) can just tell
you.
S. Ross
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Update: June 2012
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