signals and systems using matlab luis f. chaparro · 2018-02-19 · 47 what have we accomplished?...
TRANSCRIPT
![Page 1: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/1.jpg)
Signals and Systems
Using MATLAB
Luis F. Chaparro
![Page 2: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/2.jpg)
Chapter 3 - The Laplace
Transform
![Page 3: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/3.jpg)
3
What is in this chapter?
Definition of Laplace transform
Analysis of LTI systems using Laplace transform
Properties of Laplace transform
Inverse Laplace transform
Convolution integral
Convolution sum and Laplace
System interconnection
![Page 4: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/4.jpg)
4
Signals and LTI systems
![Page 5: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/5.jpg)
5
![Page 6: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/6.jpg)
6
![Page 7: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/7.jpg)
7
![Page 8: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/8.jpg)
8
![Page 9: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/9.jpg)
9
![Page 10: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/10.jpg)
10
![Page 11: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/11.jpg)
11
![Page 12: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/12.jpg)
12
One-sided Laplace Transform
![Page 13: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/13.jpg)
13
![Page 14: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/14.jpg)
14
![Page 15: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/15.jpg)
15
![Page 16: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/16.jpg)
16
![Page 17: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/17.jpg)
17
![Page 18: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/18.jpg)
18
![Page 19: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/19.jpg)
19
Linearity
![Page 20: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/20.jpg)
20
![Page 21: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/21.jpg)
21
![Page 22: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/22.jpg)
22
Derivative
![Page 23: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/23.jpg)
23
![Page 24: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/24.jpg)
24
![Page 25: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/25.jpg)
25
Time Shifting
![Page 26: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/26.jpg)
26
![Page 27: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/27.jpg)
27
Convolution integral
![Page 28: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/28.jpg)
28
Inverse Laplace Transform
![Page 29: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/29.jpg)
29
![Page 30: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/30.jpg)
30
![Page 31: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/31.jpg)
31
![Page 32: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/32.jpg)
32
![Page 33: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/33.jpg)
33
![Page 34: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/34.jpg)
34
![Page 35: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/35.jpg)
35
![Page 36: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/36.jpg)
36
![Page 37: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/37.jpg)
37
![Page 38: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/38.jpg)
38
![Page 39: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/39.jpg)
39
![Page 40: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/40.jpg)
40
![Page 41: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/41.jpg)
41
![Page 42: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/42.jpg)
42
![Page 43: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/43.jpg)
43
![Page 44: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/44.jpg)
44
![Page 45: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/45.jpg)
45
![Page 46: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/46.jpg)
46
![Page 47: Signals and Systems Using MATLAB Luis F. Chaparro · 2018-02-19 · 47 What have we accomplished? Connection of Laplace and Fourier transforms BIBO stability and pole location Steady-state](https://reader030.vdocument.in/reader030/viewer/2022040203/5e971199ff2b81553e40d556/html5/thumbnails/47.jpg)
47
What have we accomplished?
Connection of Laplace and Fourier transforms
BIBO stability and pole location
Steady-state analysis using Fourier for periodic and
aperiodic signals
Significance of complex exponentials as inputs of LTI systems
Where do we go from here?
Complex frequency analysis of signals
Convolution integral computation and transfer function
Significance of location of poles and zeros
Sinusoidal representation of periodic signals
Solution of differential equations, transient and
steady state responses, zero-input and zero-state
responses