DSP Lecture 8: Introduction to the z-Transform

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ECSE-4530  Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 8: Introduction to the z-Transform (9/22/14)

0:00:03  Review of CTFT/DTFT; what is DT version of the Laplace transform?
0:03:23  Why is z^n a special signal for DT LTI systems?
0:05:19  Introduction to the transfer function
0:06:26  How are the DTFT and z-transform related?
0:07:13  The unit circle plays a critical role for the z-transform
0:10:20  Why do we need the z-transform?
0:14:13  The region of convergence (ROC)
0:17:23  Example: the step function
0:20:43  What do ROCs look like?
0:22:58  If the ROC includes the unit circle, the system is stable
0:25:19  Poles and zeros
0:26:37  Z-transform examples
0:26:45  Right-sided exponential
0:30:16  Left-sided exponential
0:34:23  Two functions can have the same algebraic z-transform but different ROCs- specifying both is important
0:37:13  The sum of two right-sided signals
0:41:14  Right-sided plus left-sided
0:44:43  Finite-length exponential
0:52:14  Exponential times a cosine
1:00:07  ROC rules
1:04:01  The ROC, stability, and causality
1:06:49  Desirable ROCs: all poles are inside the unit circle

Follows Section 3.1 of the textbook (Proakis and Manolakis, 4th ed.).

YouTube url:	https://www.youtube.com/watch?v=ikbLAwtYE3s&list=PLuh62Q4Sv7BUSzx5Jr8Wrxxn-U10qG1et&index=8
Created:	1. 3. 2021 04:35:50

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DSP Lecture 8: Introduction to the z-Transform