**Reading:**- Chapter 5 (Geometric Signal Theory)
of
**Mathematics of the DFT** - Chapter 6 (The DFT Derived)
- Assignment 3

- Chapter 5 (Geometric Signal Theory)
of
**Lecture Videos (Total Viewing Time 2 Hours):**- Geometric Signal Theory
[25:28]
- Preview of Orthogonal Projection
[3:12]
- DFT Review, Orthogonal Projection
[15:36]
- Orthogonal Projection Example
[4:12]
- Orthogonal Projection onto Coordinate Axes
[3:38]
- Reconstruction by Summing Orthogonal
Projections, Change of Coordinates in Signal Space, Spanning
N-Space with N Orthogonal Vectors, Linear Independence, Length 2
DFT
[22:34]
- Inverse DFT as a Sum of Projections,
Normalized DFT, Gram-Schmidt Orthogonalization
[3:34]
- Nth Roots of Unity
*W*_{N}^{k}, Twiddle Factors [2:21] - Nth Roots of Unity for
*N*=8 [12:01] - DFT Sinusoids
[4:55]
- Review of DFT Sinusoid Orthogonality,
Normalization, DFT as Inner Product, IDFT as Sum of
Projections
[4:01]
- Inverse DFT Derived
[1:34]
- DFT of DFT-Sinusoids, DFT of
Non-DFT-Sinusoids, Geometric Series Closed Form, Magnitude
Spectrum, Phase Spectrum, Sinc Function, Aliased Sinc Function,
Bins, Zero Padding, Windowing
[19:13]

- Geometric Signal Theory
[25:28]

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University