The vibrations of a finite crystal is what you want. The DFT is the expansion into normal modes. -- Gene
________________________________ From: Henry Baker <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Sent: Sunday, July 28, 2013 12:13 PM Subject: [math-fun] Really stupid physics question
We've all seen the classical analysis of a vibrating string, which leads to classical Fourier theory.
In the 20th century, we all became converts to DFT's (Discrete Fourier Transforms).
So....
I'd like to see the exact mechanical counterpart to the DFT.
Given N, the _length_ of the DFT, how do I arrange for N masses & (?) Hookean springs so that the dynamics give me exactly the DFT ?
In particular, for very small N (N<10, nowhere near the continuum case), what do such systems look like?
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