DSP Lecture 3: Convolution and its properties

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 3: Convolution and its properties (9/4/14)
0:00:03 Review of impulse response
0:02:17 Running example: computing a system's response to a signal in different ways
0:03:18 Direct computation
0:05:37 Using the convolution sum: adding up shifted and scaled copies of the impulse response
0:12:31 Flipping and sliding one signal against the other
0:15:17 Matlab example of flipping and sliding
0:18:05 Understanding h[n-k]
0:23:54 The convolution array (a fast method for convolving short signals)
0:29:14 Convolving infinite-length signals
0:33:38 The sum of a finite geometric series
0:43:46 Properties of convolution/LTI systems
0:48:56 Commutative property
0:50:40 Distributive property
0:52:43 Associative property
0:55:13 Causality and the impulse response
0:57:42 The step response and its relationship to the impulse response
1:02:08 Differential and difference equations
Follows Section 2.3 of the textbook (Proakis and Manolakis, 4th ed.).