Signals and Systems Using MATLAB
Luis F. Chaparro
2
Chapter 10 - The Z-transform
3
What is in this chapter?
Laplace transform of sampled signals and Z-transform Two- and one-sided Z-transforms
Poles and zeros and region of convergence Convolution sum and transfer function
Inverse Z-transform
Solution of difference and differential equations
4
Laplace transform of sampled signals
5
Two-sided and one-sided Z-transform
6
7
Poles and Zeros
8
9
10
11
12
Convolution Sum and Transfer Function
13
14
15
16
17
18
Interconnection of discrete-time systems
Cascade
Negative feedback Parallel
19
20
One-sided Z-transform Inverse Inspection
Long-division
21
Partial Fraction Expansion
22
23
Partial Fraction Expansion with MATLAB
24
Example
25
26
Solution of Difference Equations
27
28
Solution of Differential Equations
29
30
Inverse of Two-sided Z-transforms
31
What have we accomplished?
Fourier analysis of discrete-time systems
Where do we go from here?
Connection of Laplace and Z-transforms
Solution of difference and differential equations with initial conditions Significance of poles and zeros in z-plane and poles for ROC
Application of Z-transform to control
Frequency representation of discrete-time systems Transfer function of recursive and non-recursive filters
