B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

Problems 61
(b) Determine the odd and even components of the following functions: (i) u(t); (ii) e- a t u(t);
(iii) Jt.
2.7-6 (a) If the two halves of one period of a periodic signal are of identical shape except that one is the
negative of the other, the periodic signal is said to have a half-wave symmetry. If a periodic
signal g(t) with a period T o satisfies the half-wave symmetry condition, then
g (r - :o ) = -g(t)
In this case, show that all the even-numbered harmonics (coefficients) vanish.
(b) Use this result to find the Fourier series for the periodic signals in Fig. P2.7-6.
Figure P.2.7·6
t -
- 6 -4
'(j
4
t +-
2.8-1 A periodic signal g (t) is expressed by the following Fourier series:
Jr
g(t) = 3 sin t + cos 3t - 3 + 2cos (St + 3 )
( 2:,r)
(a)
(b)
(a) By applying Euler's identities on the signal g(t) directly, write the exponential Fourier series
for g (t).
(b) By applying Euler's identities on the signal g (t) directly, sketch the exponential Fourier series
spectra.