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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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