Roymech

Fourier Expansions


Fourier Expansions

Introduction

The figures below are examples of typical periodic functions with the associated fourier series. I have also included plots generated using Mathcad illustrating what results from the series with a small mumber of terms included.


1)


Plotted from 0 to 2π with A = 4,0 and with 5 terms )







2)


                Plotted from 0 to 2π with A = 4 , α =2 and with 6 terms )






3)


Plotted from 0 to 2π with A = 4, b = 1,0 and with 5 terms





4)


Plotted from 0 to 2π with A = 4, and with 5 terms






5)



Plotted from 0 to 2π with A = 4,0, and with 5 terms.




6)


Plotted from 0 to 2π with A = 4,0 and with 5 terms



7)


Plotted from 0 to 2π with A = 4,0 and with 5 terms






8)


Plotted from 0 to 2π with A = 4,0 and with 5 terms




Useful Related Links
  1. Fourier Series ...Very clear cand comprehensive Notes
  2. Fourier Series Applet .. Applet Illustrating fourier series for different waveforms.