Experiments with MS Excel: Effects of Bandlimiting – Sawtooth Waveform 

I used the following expression for a sawtooth waveform to first generate the waveform mathematically and then try and remove the higher harmonics to band limit the signal and study the effect band-limiting had on the shape of the signal.

442a08a7d99aa42efbbba8ee8205c5b78c583ebd-01

The MS Excel file is attached here 

I set the Amplitude, A arbitrarily as 10 and the time frame from -10 to +10. Since I can’t possibly include infinite components I decided to go from k=1 to k=7 the expansion would then be as follows.

=((A2/2)((A2/3.14)*(SIN(2*3.14*100*B2)+((SIN(4*3.14*100*B2))/2)((SIN(6*3.14*100*B2))/3)+((SIN(8*3.14

*100*B2))/4)((SIN(10*3.14*100*B2))/5)+((SIN(12*3.14*100*B2))/6)((SIN(14*3.14*100*B2))/7))))

chart (1).png

This is the waveform for the signal with 6 harmonics.

Plotting the signal as I keep on cutting down on the number of components.

chart (8)

chart (9)

chart (10)

chart (11)

 

The equation for the signal with only the 1st component would look like this:

   =((A2/2)((A2/3.14)*(SIN(2*3.14*100*B2)+(SIN(4*3.14*100*B2))/2)))

And finally the band-limited signal: taking only the case: k=1 and neglecting all other higher harmonics.

=((A2/2)+((A2/3.14)*SIN(2*3.14*100*B2)))chart (2).png

This would be the effect of a filter that removes all the higher components from a sawtooth waveform i.e it is reduced to a sine wave.

 

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