DSP Lecture 8: Introduction to the z-Transform

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.).