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.