ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 13: The Sampling Theorem (10/16/14)
0:00:02 The sampling theorem
0:02:25 Periodic sampling of a continuous-time signal
0:04:22 Non-ideal effects
0:07:54 Ways of reconstructing a continuous signal from discrete samples
0:10:02 Nearest neighbor
0:10:39 Zero-order hold
0:11:26 First-order hold (linear interpolation)
0:12:41 Each reconstruction algorithm corresponds to filtering a set of impulses with a specific filter
0:18:25 What can go wrong with interpolating samples?
0:20:54 Matlab example of sampling and reconstruction of a sine wave
0:23:37 Bandlimited signals
0:25:10 Statement of the sampling theorem
0:26:29 The Nyquist rate
0:27:50 Impulse-train version of sampling
0:30:18 The FT of an impulse train is also an impulse train
0:32:38 The FT of the (continuous time) sampled signal
0:34:42 Sampling a bandlimited signal: copies in the frequency domain
0:37:19 Aliasing: overlapping copies in the frequency domain
0:39:36 The ideal reconstruction filter in the frequency domain: a pulse
0:41:06 The ideal reconstruction filter in the time domain: a sinc
0:42:43 Ideal reconstruction in the time domain
0:43:37 Sketch of how sinc functions add up between samples
0:45:45 Example: sampling a cosine
0:51:43 Why can't we sample exactly at the Nyquist rate?
0:54:49 Phase reversal (the "wagon-wheel" effect)
0:58:31 Matlab examples of sampling and reconstruction
0:58:41 The dial tone
1:03:43 Ringing tone
1:05:27 Music clip
1:10:25 Prefiltering to avoid aliasing
1:11:48 Conversions between continuous time and discrete time; what sample corresponds to what frequency?
Follows Section 6.1 of the textbook (Proakis and Manolakis, 4th ed.).