# Solved Problems-4

Problems-4

Find the trigonometric Fourier series for the waveform shown in figure and sketch the spectra.

Solution

Here, ; for 0 <
= 0; for
â‡’
â‡’
; for
= 0 ; for
â‡’
= ; for
= ; for
âˆ´

The even harmonic amplitudes are given directly by

But, the odd harmonic amplitudes are given by computation
âˆ´ = = 0.1885 V
and
= â€“ 0.08 V

*Ï‰t*<*Ï€*and*Ï€*<*Ï‰ t*< 2*Ï€**n*odd.*n*even.*n*even.*n*odd.**Line Spectra**The even harmonic amplitudes are given directly by

*b*coefficients, since there are no even cosine terms._{n}*C*_{2}= ,*C*_{4}= = â€“0.0397 V