Approximating floor()

Most of those functions act like step functions. You can take the first 2 or 3 terms of the Fourier Series expansion of a step function to turn a step function into a continuous function. It might not be a pretty continuous function, but it does basically do what you ask, .

There''s a demonstration of this in Java here:

http://www.math.ubc.ca/~feldman/demos/demo3.html

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Thanks! That would be what I was looking for. Now I just have to figure out how to do an actual Fourier Transform. My calculus is a little rusty. Thanks again.

cyn

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Original post by grhodes_at_work
Most of those functions act like step functions. You can take the first 2 or 3 terms of the Fourier Series expansion of a step function to turn a step function into a continuous function. It might not be a pretty continuous function, but it does basically do what you ask, .

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Doesn''t the Fourier Series only work for functions that repeat? It won''t really work for "floor".

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Original post by cyn
Thanks! That would be what I was looking for. Now I just have to figure out how to do an actual Fourier Transform. My calculus is a little rusty. Thanks again.

cyn

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Fourier Series is different from Fourier Transform. Here''s a link. (But according to that link, as I said, Fourier Series can only represent periodic functions).

The Fourier series will create a periodic function; however, you can use it for any function, even a non-repeating one, over a finite domain to get an approximation of that function over the domain. The width of the domain will turn out to be a characteristic wavelength of the Fourier series, e.g., a function that starts out non-periodic will repeat at a wavelength equal to the domain you create the Fourier series over.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.