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Fourier Transforms

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Hi. I was recently researching different things in math and computer science and have stumbled on Fourier transformations. I understand the basics, when I have a noise functions Fourier transformations break them up into a bunch of sines of different frequencies that make up an original function when added up. But what''s the point behing the Fourier transforms? Why are they helpful and how can they be used? Any help would be appreciated. Thanks.

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You use a transform to make solving a problem easier. A simplier example than a fourier transform would be using polar or spherical coordinates in an integral. A little closer to a fourier transform would be term by term integration of the series expansion of a function. I don''t know what else fourier transforms are used for but one use is solving certain types of partial differential equations. As far as a path to understanding that use of it you need to understand the series section of Calculus II first. Then you need to understand using Laplace transforms to solve ordinary differential equations. That prepares you for understanding series solutions to ordinary differential equations. I haven''t taken advanced calculus, but you might run into it there as well.

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The DFT (Discrete Fourier Tranform) takes a digitized signal from the (real) time domain into the (complex) frequency domain. An FFT is a Fast Fourier Transform, which makes digital signal processing feasible - it is subject to certain constraints that allow algorithm optimization. Most often this is the limitation that the input length must be a power of 2. It is possible to construct an FFT that works on any power and thier combinations, though it is not a trivial operation (radix based FFT).

Once you have a signal in the frequency domain, you can analyze it in ways you couldn''t have in the time domain. MPEG encoders make use of 2D FFTs, and perform JFTA (Joint Frequency-Time analysis) to build prediction vectors. (They also use the DCT (Discrete Cosine Transformation) which is related to the FFT, to perform the actual compression).

The digital EQ that WinAmp displays was produced by a variant of an FFT. (FFTs are computationally expensive, so you take short-cuts when you can).

In short, as v71 said, everywhere in digital signal processing.

AS LBW mentioned, fourier transforms are used to solve partial differential equations, which rear thier ugly heads in collision detection and any (other) type of physics simulation. Though they''re not used in the simulation directly, they''re used on the physics equations to yield the equation you need to solve-for in the simulation.

Magmai Kai Holmlor

"Oh, like you''ve never written buggy code" - Lee

"What I see is a system that _could do anything - but currently does nothing !" - Anonymous CEO

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