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ECE 4213/5213
MODULE 3
Index
1. Distribution Theory and the Dirac Delta ............................................3.0 – 3.23
2. Derivative of a Distribution, δ’(t) .......................................................3.23 – 3.24
3. Riemann-Lebesgue Lemma ................................................................3.25 – 3.29
4. Time Domain Representation of Continuous-Time Signals ...............3.29 – 3.32
5. Eigenvalues, Eigenvectors, Eigenfunctions ........................................3.33 – 3.34
6. Spectral Basis and Fourier Transform ................................................3.35 – 3.39
7. Frequency Response ..........................................................................3.40 – 3.43
8. Effect of Multiplying a Sinusoid times a Complex Eigenvalue ...........3.44 – 3.46
9. Distributional Fourier Transforms .....................................................3.47 – 3.52
10. Symmetry Properties of the Fourier Transform ................................3.53 – 3.54
11. More Fourier Transform Properties ..................................................3.55 – 3.59
12. Uncertainty Principle, Proof of the Heisenberg-Weyl Inequality ......3.60 – 3.88
13. Discrete-Time Fourier Transform (DTFT) ...........................................3.89 – 3.98
14. Spectral Phase, Generalized Phase, Phase Unwrapping ...................3.99 – 3.101
15. DTFT of δ[n] ........................................................................................3.102 – 3.103
16. Symmetry of the DTFT .......................................................................3.104 – 3.105
17. Some DTFT Pairs.................................................................................3.106 – 3.107
18. DTFT Properties ..................................................................................3.108 – 3.111
19. Sinusoid Times a Complex Eigenvalue (Discrete Time) .....................3.112 – 3.114
20. Discrete-Time LTI System Connections ..............................................3.115 – 3.117
21. Gain Function .....................................................................................3.117
22. Phase Delay and Group Delay, Linear Phase .....................................3.118 – 3.120
23. FIR & IIR Filters ...................................................................................3.121 – 3.125
24. Phase Response, the FIR Linear Phase Trick ......................................3.126 – 3.129
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