Discrete-Time Fourier Methods M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1
Discrete-Time Fourier Methods M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1.
Dec 21, 2015
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Discrete-Time Fourier Methods
M. J. Roberts - All Rights Reserved. Edited
by Dr. Robert Akl
1
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
2
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
3
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
4
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
5
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
6
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
7
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
8
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
9
Discrete-Time Fourier Series Concept
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
10
Discrete-Time Fourier Series Concept
The Discrete-Time Fourier Series
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
11
The Discrete Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
12
The Discrete Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
13
The Discrete Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
14
DFT Example
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
15
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
16
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
17
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
18
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
19
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
20
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
21
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
22
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
23
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
24
The DFT Harmonic Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
25
Convergence of the DFT
• The DFT converges exactly with a finite number of terms. It does not have a “Gibbs phenomenon” in the same sense that the CTFS does
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
26
The Discrete Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
27
DFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
28
DFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
29
DFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
30
The Dirichlet Function
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
31
DFT Pairs
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
32
The Fast Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
33
The Fast Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
34
Generalizing the DFT for Aperiodic Signals
Pulse Train
This periodic rectangular-wave signal is analogous to thecontinuous-time periodic rectangular-wave signal used toillustrate the transition from the CTFS to the CTFT.
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
35
DFT of Pulse Train
As the period of the rectangular wave increases, the period of the DFT increases
Generalizing the DFT for Aperiodic Signals
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
36
NormalizedDFT of
Pulse Train
Generalizing the DFT for Aperiodic Signals
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
37
The normalized DFT approaches this limit as theperiod approaches infinity.
Generalizing the DFT for Aperiodic Signals
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
38
Definition of the Discrete-Time Fourier
Transform (DTFT)
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
39
The Discrete-Time Fourier Transform
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
40
DTFT Pairs
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
41
The Generalized DTFT
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
42
The Generalized DTFT
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
43
The Generalized DTFT
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
44
Forward DTFT Example
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
45
Forward DTFT Example
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
46
Forward DTFT Example
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
47
More DTFT Pairs
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
48
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
49
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
50
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
51
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
52
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
53
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
54
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
55
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
56
DTFT Properties
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
57
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
58
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
59
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
60
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
61
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
62
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
63
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
64
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
65
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
66
Transform Method Comparisons
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
67
The Four Fourier Methods
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
68
Relations Among Fourier Methods
Multiplication-Convolution Duality
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
69
Relations Among Fourier Methods
Parseval’s Theorem
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
70
Relations Among Fourier Methods
Time and Frequency Shifting
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
71
Relations Among Fourier Methods
M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl
72
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