# Solved Problems-1

Problems-1

Determine the Fourier series for the square waveform shown below and plot the magnitude and the phase spectra.

Solution

The waveform,

*f*(*t*) =*V*; 0 <*t*<*T*/4= â€“

=

*V*;*T*/4 <*t*< 3*T*/4=

*V*; 3*T*/4 <*t*<*T*Obviously, the given function is an even function.

âˆ´

Now,

âˆ´

*b*= 0_{n}Now,

*a*_{0}=*a*=

_{n}=

=

=

= ; for

*n*= 1, 5, 9,â€¦â€¦â€¦= ; for

*n*= 3, 7, 11,â€¦â€¦â€¦= 0; for

*n*= 2, 4, 6,â€¦â€¦â€¦So,

*f*(*t*) =*Ans.***Magnitude Spectra****Phase Spectra**