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Solved Problems-1

Problems-1
Determine the Fourier series for the square waveform shown below and plot the magnitude and the phase spectra.
 
Description: Description: 1089.png
 
Solution
The waveform, f (t) = V; 0 < t < T/4
= – VT/4 < t < 3T/4
V; 3T/4 < t < T
 
Obviously, the given function is an even function.
∴ bn = 0

Now, a0 = Description: Description: 2716.png
an = Description: Description: 2723.png
 
Description: Description: 2729.png
 
Description: Description: 2735.png
 
Description: Description: 2741.png Description: Description: 2747.png
 
Description: Description: 2753.png; for n = 1, 5, 9,………
 
Description: Description: 2759.png; for n = 3, 7, 11,………
 
= 0; for n = 2, 4, 6,………
 
So, f (t) = Description: Description: 2769.png Ans.

Magnitude Spectra
 
Description: Description: 1142.png
 
Phase Spectra
 
Description: Description: 1150.png
 





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