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