Frequency Domain Analysis
Part II
Dr. Mohamed Refky Amin
Electronics and Electrical Communications Engineering Department (EECE)
Cairo University
http://scholar.cu.edu.eg/refky/
OUTLINE
• Previously on ELC 202B
• Parseval’s Theorem
• Trigonometric Fourier Series
• Symmetry Considerations
Dr. Mohamed Refky 2
Previously on ELC 202B
3Dr. Mohamed Refky
Spectra of Continuous Time Signals
Time domain Representation
Frequency domain Representation
Single-sided Frequency
Spectrum
Previously on ELC 202B
4Dr. Mohamed Refky
Spectra of Continuous Time Signals
Double-sided Frequency Spectrum
Previously on ELC 202B
5Dr. Mohamed Refky
Representation of Signals Over an Interval
Previously on ELC 202B
6
If the expansion interval equals the length of the period of a
periodic signal, the Fourier series expansion holds for the whole
signal (if it satisfies the previous conditions). This is because the
expansion has a periodic form.
Dr. Mohamed Refky
Fourier Series of Periodic Signals
Previously on ELC 202B
7Dr. Mohamed Refky
Exponential (Complex) Fourier Series of
Periodic Signals
Frequency Domain
8
Parseval’s Theorem
Dr. Mohamed Refky
Frequency Domain
9Dr. Mohamed Refky
Parseval’s Theorem
Frequency Domain
10Dr. Mohamed Refky
Parseval’s Theorem
Orthogonal
components
Frequency Domain
11Dr. Mohamed Refky
Parseval’s Theorem
Frequency Domain
Dr. Mohamed Refky
Parseval’s Theorem
Frequency Domain
Dr. Mohamed Refky
Parseval’s TheoremParseval’s Theorem can be used to determine the power contained
in a certain range of frequency in the frequency spectrum of the
signal.
Frequency Domain
14Dr. Mohamed Refky
Example (1)
Frequency Domain
15Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
16Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
17Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
18Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
19Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
20Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
21Dr. Mohamed Refky
Trigonometric Fourier Series
Frequency Domain
22
Find the Fourier series representation of the sawtooth signal
shown below
Example (2)
Dr. Mohamed Refky
Frequency Domain
23
Symmetry Considerations
Dr. Mohamed Refky
Frequency Domain
24
Symmetry Considerations
Dr. Mohamed Refky
Frequency Domain
25
Symmetry Considerations
Dr. Mohamed Refky
Frequency Domain
26
Symmetry Considerations
Dr. Mohamed Refky
