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The DFT, Cont'd

There are several ways to think about the DFT:
  1. Projection onto the set of ``basis'' sinusoids (frequencies at $ N$ roots of unity)
  2. Coordinate transformation (``natural'' $ R^N$ basis to ``sinusoidal'' basis)
  3. Matrix multiplication $ \underline{X} = \mathbf{W}^\ast \underline{x}$ ,
    where $ \mathbf{W}^\ast[k,n]=e^{-j\omega_k t_n}$
  4. Sampled uniform filter bank output
This course will emphasize interpretations 1 and 4.


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``Review of the Discrete Fourier Transform (DFT)'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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