Download presentation
Presentation is loading. Please wait.
1
Pertemuan 13 Transformasi - Z
2
Z-Transform Introduction Y(s) y(t) U(s) u(t) G(s) Linear system
Tools to analyse continuous systems : Laplace transform It could be used for sampled or discrete systems t X T
3
Z-Transform t Apply Laplace transform of f’(t)
Factors like Exp(-sT) are involved Unlike the majority of transfer functions of continuous systems It will not lead to rational functions
4
Z-Transform Definition
5
Summary The operation of taking the z-transform of a continuous-data
function, f(t), involves the following three steps: 1- f(t) is sampled by an ideal sampler to get f’(t) 2- Take the Laplace transform of f’(t) 3- Replace by z in F’(s) to get
6
Mapping between the s-plane and the z-plane
Primary strip Imz z-plane 1 Rez The left half of the primary strip is mapped inside the unit circle
7
Mapping between the s-plane and the z-plane
Primary strip Imz Z-plane Rez 1 The right half of the primary strip is mapped outside the unit circle
8
Mapping between the s-plane and the z-plane
Complementary strip Imz Z-plane Rez 1 The right half of the complementary strip is also mapped inside the unit circle
9
s-plane properties of F’(s)
Complementary strip Complementary strip Primary strip Complementary strip Complementary strip
10
s-plane properties of F’(s)
Complementary strip X Complementary strip X Primary strip X Complementary strip X Complementary strip X X Poles of F’(s) in primary strip
11
s-plane properties of F’(s)
Complementary strip X Folded back poles Complementary strip X Primary strip X Complementary strip X Complementary strip X X Poles of F’(s) in complementary strips
12
The constant damping loci
s-plane z-plane
13
The constant frequency loci
s-plane z-plane
14
The constant damping ratio loci
Imz Rez s-plane z-plane
15
The constant damping ratio loci
Imz Rez s-plane z-plane
16
Mapping between the s-plane and the z-plane
Conclusion: All points in the left half of the s-plane are mapped into the Region inside the unit circle in the z-plane. The points in the right half of the s-plane are mapped into the Region outside the unit circle in the z-plane
17
Example: discrete exponential function
k 1 Apply z-transform
18
Series Reminder
19
Example: discrete Cosine function
20
Another approach
21
Dirac function
22
Sampled step function t u(t) 1 NB: Equivalent to Exp(-k) as 0
23
Delayed pulse train T t t
24
Complete z-transform Example:exponential function
34
Terima kasih Terima kasih
Similar presentations
![10.0 Z-Transform 10.1 General Principles of Z-Transform linear, time-invariant Z-Transform Eigenfunction Property y[n] = H(z)z n h[n]h[n] x[n] = z n.](/23/6636408/big_thumb.jpg "10.0 Z-Transform 10.1 General Principles of Z-Transform linear, time-invariant Z-Transform Eigenfunction Property y[n] = H(z)z n h[n]h[n] x[n] = z n.>")