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- Reading:
- 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]
- You should now understand how the twisted signal plot
``pancakes'' to produce the DFT displayed on the complex-plane at time zero
in the WebGL Spectrum Analyzer
- Inverse DFT as a Sum of Projections,
Normalized DFT, Gram-Schmidt Orthogonalization
[3:34]
- Nth Roots of Unity WNk, 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]
- You should now understand how the phase-rotated signal in the
complex-plane versus time display is summed to the green front complex-plane in the WebGL
Spectrum Analyzer
- Supplementary flipped-class lecture on the inner product and its applications:
- Part 1/2
[49:45]
- Part 2/2
[47:22]
- Image Credits:
- Deep Neural Net: https://i.stack.imgur.com/OH3gI.png
- FFT Butterfly: http://www.cmlab.csie.ntu.edu.tw/cml/dsp/training/coding/transform/fft.html
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