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# Just a llittle wave help

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I am reading a book on quantum reality, and in there it states that any wave (specifically, proxy waves) can be built with any number of carefully tweaked sin waves, impulse waves, etc. My question is how would I go about breaking a wave into its sin components?

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I don''t know exactly how you do this, but there is a principle (I believe it''s called the Superposition Principle) that states that any two (or more) waves that converge will cause a resultant wave that is the sum of the converging waves'' crests and troughs. Sorry if that sounds a little confusing

Basically, let''s say you have a wave with equation y = sin x, and another one that''s y = cos x. Because when there''s a crest for sin x, there''s a trough for cos x, the two waves will cancel out and there will be "no" wave.

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You can break wave to its sin components using Fourier series.
Any periodic function f(x) can be written as infinite sum of sine and cosine waves, each wave has its own coefficient. It goes something like this:
f(x) = sum(An*sin(n*PI*x/L)+Bn*sin(n*PI*x/L))

L - function period, n changes from 0 to infinity

To find An and Bn you need to calculate integrals:

An=(2/L)*I(f(x)sin(n*x*PI/L)dx)
Bn=(2/L)*I(f(x)cos(n*x*PI/L)dx)

Integration limits are -L/2 and L/2

Hope it helps you.

K

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This is a good starting point. I know I found the full source code to a fft sometime in the past, but I really don''t remember where.

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Also, note that the regular (non-fast) fourier transform algorithm is much easier to understand and/or do by hand on notebook paper than the FFT. Don''t bother reading about the Fast Fourier Transform unless you are going to be writing a program to do this.

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