Continuous-time Fourier series (CTFS)

Example #1: triangle wave

Define and plot triangle wave 
[Graphics:../Images/index_gr_16.gif]

[Graphics:../Images/index_gr_17.gif]

Complex Fourier series 
[Graphics:../Images/index_gr_18.gif]
[Graphics:../Images/index_gr_19.gif]
Real representation 
[Graphics:../Images/index_gr_20.gif]
[Graphics:../Images/index_gr_21.gif]
Plot result 
[Graphics:../Images/index_gr_22.gif]

[Graphics:../Images/index_gr_23.gif]

Plot error between truncated Fourier series and triangle wave 
[Graphics:../Images/index_gr_24.gif]

[Graphics:../Images/index_gr_25.gif]

Frequency domain plots 
[Graphics:../Images/index_gr_26.gif]
[Graphics:../Images/index_gr_27.gif]

[Graphics:../Images/index_gr_28.gif]

Example #2: sawtooth wave

Define and plot square wave 
[Graphics:../Images/index_gr_29.gif]

[Graphics:../Images/index_gr_30.gif]

Complex Fourier series 
[Graphics:../Images/index_gr_31.gif]
[Graphics:../Images/index_gr_32.gif]
Real representation 
[Graphics:../Images/index_gr_33.gif]
[Graphics:../Images/index_gr_34.gif]
Plot result 
[Graphics:../Images/index_gr_35.gif]

[Graphics:../Images/index_gr_36.gif]

More terms 
[Graphics:../Images/index_gr_37.gif]

[Graphics:../Images/index_gr_38.gif]

[Graphics:../Images/index_gr_39.gif]
Even more terms 
[Graphics:../Images/index_gr_40.gif]

[Graphics:../Images/index_gr_41.gif]

[Graphics:../Images/index_gr_42.gif]
Frequency domain plots 
[Graphics:../Images/index_gr_43.gif]
[Graphics:../Images/index_gr_44.gif]

[Graphics:../Images/index_gr_45.gif]

[Graphics:../Images/index_gr_46.gif]

[Graphics:../Images/index_gr_47.gif]

Example #3: square wave

Define and plot square wave 
[Graphics:../Images/index_gr_48.gif]

[Graphics:../Images/index_gr_49.gif]

Complex Fourier series 
[Graphics:../Images/index_gr_50.gif]
[Graphics:../Images/index_gr_51.gif]
Real representation 
[Graphics:../Images/index_gr_52.gif]
[Graphics:../Images/index_gr_53.gif]
Plot result 
[Graphics:../Images/index_gr_54.gif]

[Graphics:../Images/index_gr_55.gif]

More terms 
[Graphics:../Images/index_gr_56.gif]

[Graphics:../Images/index_gr_57.gif]

[Graphics:../Images/index_gr_58.gif]
Even more terms 
[Graphics:../Images/index_gr_59.gif]

[Graphics:../Images/index_gr_60.gif]

[Graphics:../Images/index_gr_61.gif]
Frequency domain plots 
[Graphics:../Images/index_gr_62.gif]
[Graphics:../Images/index_gr_63.gif]

[Graphics:../Images/index_gr_64.gif]

[Graphics:../Images/index_gr_65.gif]

[Graphics:../Images/index_gr_66.gif]

Converted by Mathematica      March 24, 2003