frequency domain analysis part ii frequency domain analysis part ii dr. mohamed refky amin...
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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
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Previously on ELC 202B
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Spectra of Continuous Time Signals
Time domain Representation
Frequency domain Representation
Single-sided Frequency
Spectrum
Previously on ELC 202B
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Spectra of Continuous Time Signals
Double-sided Frequency Spectrum
Previously on ELC 202B
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Representation of Signals Over an Interval
Previously on ELC 202B
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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.
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Fourier Series of Periodic Signals
Previously on ELC 202B
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Exponential (Complex) Fourier Series of
Periodic Signals
Frequency Domain
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Parseval’s Theorem
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Frequency Domain
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Parseval’s Theorem
Frequency Domain
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Parseval’s Theorem
Orthogonal
components
Frequency Domain
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Parseval’s Theorem
Frequency Domain
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Parseval’s Theorem
Frequency Domain
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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
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Example (1)
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Trigonometric Fourier Series
Frequency Domain
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Find the Fourier series representation of the sawtooth signal
shown below
Example (2)
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Frequency Domain
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Symmetry Considerations
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Frequency Domain
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Symmetry Considerations
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Frequency Domain
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Symmetry Considerations
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Frequency Domain
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Symmetry Considerations
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