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