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Signals and Systems
Using MATLAB
Luis F. Chaparro
Chapter 4 - Frequency Analysis
The Fourier Series
3
What is in this chapter?
Eigenfunctions and LTI systems
Properties of Fourier Series
Complex and trigonometric Fourier Series
Line spectrum: distribution of power over frequency
Response of LTI systems to periodic signals
Laplace and Fourier Series
4
Eigenfunctions revisited
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Application in
communications
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input sinusoid
ss output sinusoid
of same frequency
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input
output
magnitude and phase at
harmonic frequency
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What have we accomplished?
Connection of Laplace and Fourier transforms
Response of LTI systems to periodic signals
Extension of Fourier representation for aperiodic signals
Unification of spectral theory for periodic and aperiodic signals
Where do we go from here?
Sinusoidal representation of periodic signals
Eigenfunction property of LTI systems
Convolution and frequency response of LTI systems
Connection of Fourier series and Laplace transform
Inverse time frequency relation
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