Visualizing the Discrete Fourier Transform

Re:Visualizing the Discrete Fourier Transform by 4ad on Thursday September 24, 2015 @03:33PM (#10274050)

If you understand DFT, it should be very easy to understand FFT. It's the same thing but with an infinite-dimensional vector space. The fact that it's a vector space is the important thing. The infinite dimensionality is relatively a minor detail.

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Re:Visualizing the Discrete Fourier Transform by ablatner on Thursday September 24, 2015 @07:13PM (#10275434)

No that's not right. The FFT is not infinite dimensional. It's the same dimension as whatever length FFT you take. The FFT is just a set of algorithms for computing the DFT. In general they work by recursively decomposing an N-length DFT into shorter length DFT's.

The DTFT on the other hand is "infinite" dimensional in that it takes an infinite time series as input and outputs a continuous spectrum with period of 2pi.

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Re:Visualizing the Discrete Fourier Transform by 4ad on Friday September 25, 2015 @06:42AM (#10277327)

Sorry, This is embarrassing, I must have not drank my coffee... Of course you are right.

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Re:Visualizing the Discrete Fourier Transform by blt on Thursday September 24, 2015 @08:48PM (#10275835)

I was talking about the O(n log n) algorithm that computes the DFT.

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Re:Visualizing the Discrete Fourier Transform by 4ad on Friday September 25, 2015 @06:43AM (#10277334)

Yeah, see my other comment.

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