If the two halves of one period of a periodic signal are identical in shape except that the one is the negative of the other, the periodic signal is said to have a half-wave symmetry. If a periodic Figure P2.8-4 signal g(t) with a period To satisfies the half-wave symmetry condition, then an = -6 In this case, show that all the even-numbered harmonics vanish, and that the odd-numbered harmonic coefficients are given by 4 To J To/2 -T 1 8(1-To) g(t) cos nwot dt and bn = Use these results to find the Fourier series for the periodic signals in Fig. P2.8-4. e-1/10 = 2 -g(t) T ANAZ. 6 8 10 4 4 To/2 To Jo g(t) sin nwot dt (a) (b)