Signals and Systems

Using MATLAB

Luis F. Chaparro

Chapter 3 - The Laplace Transform

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

4

Signals and LTI systems

5

6

7

8

9

Three

10

11

12

One-sided Laplace Transform

13

14

15

16

17

18

19

Linearity

20

21

22

Derivative

23

24

25

Time Shifting

26

27

Convolution integral

28

Inverse Laplace Transform

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

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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