**Reading:**- Chapter 7 (Fourier Theorems for the DFT)
of
**Mathematics of the DFT** - Appendix B (Fourier Transforms for Continuous/Discrete Time/Frequency)
- Filters and Convolution
- Assignment 4

- Chapter 7 (Fourier Theorems for the DFT)
of
**Lecture Videos (Total Viewing Time 4 Hours):**- Signal and Spectra Notation for the DFT
Theorems
[5:14]
- Review of DFT as a change of coordinates,
Periodic Extension versus Time Limited Signal Windows, DFT
interpolation between spectral samples, ``spectral splatter''
in DFT of non-DFT-sinusoids
[20:44]
- Windowed Signal Segment Gives One Time Sample in the Time-Frequency Distribution
[1:28]
- DFT Linearity, Flip Operator (index reversal),
Flip Theorem, Real Signals have Hermitian (conjugate symmetric)
Spectra, Fourier Duality
[23:31]
- DFT Symmetry Theorems, Even and Odd Functions,
DCT & DST, ``Zero-Phase'' Spectra
[34:18]
- Shift Operator, Shift Theorem,
Linear Phase Terms, Convolution Thm Preview
[11:16]
- Circular Convolution, Commutativity of
Convolution, Graphical Convolution, Convolution Reverb, Impulse
Response, Convolution Representation of Linear Time-Invariant
(LTI) Filters, Convolution Theorem Stated
[36:59]
- Aliasing Demo
[4:13]
*Continuous*Graphical Convolution Demo [11:15]- Convolution Theorem Proof, FFT Convolution,
Filter Frequency Response
[21:41]
- Dual of Convolution Theorem, Application to Time-Domain
Windowing
[6:00]
- Review/FAQ Presented 11/11/2014: Why Vector
Spaces, Signal Energy as Length Squared, Power, RMS, Shift
Theorem, Convolution Theorem
[26:34]
- Correlation, Lagged Product, Correlation Thm,
Autocorrelation
Power Spectrum
[6:42]
- Power Thm, Parseval's Thm
[7:50]
- Normalized DFT (NDFT)
[7:04]
- Review of Linearity, Flip, Symmetry, Shift,
Convolution, Correlation, and Power Theorems
[19:51]
- [Optional] Intuitive Explanation of the Sampling Theorem
[14:57]
- Scaling Theorem (continuous time),
Stretch Operator, Stretch Thm, Filter Guard Bands,
Discrete-Time Stretch Thm, Downsampling, Aliasing,
Downsampling Theorem
[31:36]

- Signal and Spectra Notation for the DFT
Theorems
[5:14]

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