Signals and Systems

Using MATLAB

Luis F. Chaparro

Chapter 5 - Frequency

Analysis

The Fourier Transform

3

What is in this chapter?

From Fourier series to Fourier

transform

Spectral representation of periodic and aperiodic signals

Existence of Fourier

transform

Fourier and Laplace

transforms

Modulation and signal

transmission

Time frequency relations and Fourier transform

Convolution and

Filtering

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

Full-

wave

rectifier

Low-pass

filter

23

24

25

26

27

28

29

30

31

32

What have we accomplished?

Convolution and Filtering

Application of Laplace analysis and transient

response

Application of Fourier analysis and steady state response

Where do we go from here?

Unification of frequency representation of periodic and

aperiodic signals

Duality in time and frequency

Frequency response of LTI systems

Connection of Fourier series and Laplace

transformInverse time frequency

relation

Application of time-frequency relation in sampling theory

Filter design