Question

3.) Expand the function consisting of a train of pulses of width Tp into Fourier series: (A for – 7 < t < 1 2 f(t) = {o for <t< , lo for the < t < 1 / 1 where T is the period of the function and T, < T.

Answer 1

Solution

Function is even thus cosine Fourier series.

Sodupion The Fourier coefficients are given 110 as- I front, and the fores con ( 2art) de, ben je in erat) de -T12 Here given the periodic function, fe- Go, 1/₂ LE C-TP/2 L A - T/p/2 CAC TP/2 o TP/2 LECT/2 Tp 7 NV This Sine the function is ever kunctions about to fl-t) - fce), It will have asly ao and cosine coefficents as Cosine series]. This boo - 1 L T - T, o TP. a ferese - Closer Tore & fim de 7 (0+o+A (2 7 + [als + 1)] a = ATP O TP2 and 4 and ( & corect Joacetes - Josifa) a fan ovet, de ( mat ae] Otot A y pl2 (27) s (1979) +sm 1976)) {w-x) =<sme} an 2*() forurier series as Thus, giver kunctions can be expanded in cosine f(t)- Act an cos (ant). I 7. 2 fees : ATP + ad sin (To) cos (1 )