Experiments with MS Excel: Effects of Bandlimiting – Triangular Waveform

I used the following expression for a triangular 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.

NumberedEquation1.gif

The MS Excel file is attached here 

The time frame is taken to be from -10 to +10. Since I can’t possibly include infinite components I decided to go for the first 5 harmonics, the expansion would then be as follows.

=(D2((A2/121)*(SIN(22*3.14*100*B2))))

chart (13).png

This is the waveform for the signal with 5 harmonics.

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

chart (14).png

chart (15).png

chart (16).png

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

=(H2((A2/9)*(SIN(6*3.14*100*B2))))

chart (17).png

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

=(A2*(SIN(2*3.14*100*B2)))

chart (18).png

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s