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Fourier Series
4.2-4.3
Motivation
(Time Domain Representation)
(Frequency Domain Representation)
Goal
Connection to Calc
(Taylor Series)
Introductory Example
Details
Fourier Coefficients
Methods of Calculating the Fourier Series Coefficients
Fourier Series of Impulse Train
Fourier Series of Impulse Train
Fourier Series of a Square Wave
Co is a DC average.
Details (1)
Details (2)
Details (3)
Gibbs Phenomenon
Gibbs Phenomenon (2)
Fourier Series Coefficient
K=-5, Ck=2jV/(5π)K=-3, Ck=2jV/(3π)K=-1, Ck=2jV/πK=1, Ck=-2jV/πK=3, Ck=-2jV/(3π)K=5, Ck=-2jV/(5π)
Frequency Spectra
K=-5, Ck=2jV/(5π)K=-3, Ck=2jV/(3π)K=-1, Ck=2jV/πK=1, Ck=-2jV/πK=3, Ck=-2jV/(3π)K=5, Ck=-2jV/(5π)
Use Matlab to Calculate Fourier Series Coefficient
Integration from 0.5 to 1
Different Representations of Fourier Series
Rectangular Pulse
Sinc Function
Spectrum for a Rectangular Pulse Train
Peak Values of Sinc x