Chapter 3 contents
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Outline of a chapter in Phil's Spectral Theory Book, kept in the 2003 edits folder. It lists sections 20 to 34: sampled signals and image spectra, digital filters, the digital Fourier transform, the Z transform, amplitude modulated pulse trains, aperture correction, the DFT and its symmetries, Parseval's theorem, a Maple example, the FFT, and the Nyquist sampling theorem.
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Table of Contents for Chapter 3 "Sampled Signals" 3.15.03
Definitions of T1, ∆t, 1 and tn. 1
20. Sampled signals and their Image Spectra. 1
Figure 20.1: non-overlapping image spectra 2
Figure 20.2: overlapping image spectra 3
21. Digital filters and their Image Spectra. 3
22. The Digital Fourier Transform X'() . 6
23. Relation between X'() and X(). 7
Digital Fourier Transform Summary Box 10
24. The Z Transform. 11
(a) convolution 12
(b) unit impulse 12
(c) time translation : D flip-flops and z-1 12
(d)derivative limit 13
(e) digital RC filter, impulse response 13
(f) poles imply feedback
Figures showing sample FIR and IIR filters. 14
(g) scramblers
Z Transform Summary Box 16
25. Amplitude Modulated Pulse Trains. 16
Pulse Train summary box 17
26. A simple application: aperture correction. 18
Figure 26.1: aperture illustration t 18
Figure 26.1: aperture illustration 19
27. The Discrete Fourier Transform (DFT) 19
Discrete Fourier Transform Summary Box 23
Figure 27.1: The pulse Pulse(t) 24
Figure 27.2: resulting pulse train 24
Figure 27.3: sampled pulse 25
Figure 27.2: sampled pulse train 25
28. Alternate Form of the DFT. 27
29. Symmetry relation for the DFT coefficients 28
30. Parseval's Theorem for the DFT 28
31. Example of a DFT using Maple 29
32. The FFT 31
33. Lee & Messerschmitt Notation 31
34. The Nyquist Sampling Theorem 33
box(t) as sinc function 33