Determine whether or not each of the following signals is pe

Determine whether or not each of the following signals is periodic. If the signal is periodic determine its fundamental period (or frequency). x(t) = Even[sin(4 pi t)u(t)] x(t) = sigma^n rightarrow infinity_n rightarrow -infinity e^-(3t - n)u(3t - n) x[n] = cos(pi n/2)cos(pi n/4) x[n] = 2 sin(pi n/4) + cos(pi n/8) - 2 cos (pi n/2 + pi/3)

Solution

The amplitudes and phase shifts are only a distraction; the first function has the same period as cos(4t), which would be pi/2.

The second function might be rewritten by using the identity
cos(2A) = 2 cos^2(A) - 1, or
(1/2) cos(2A) + (1/2) = cos^2(A).
Hence, your function is
(1/2) cos(4t - 2 pi/3) + (1/2)
and again the amplitude and BOTH shifts are irrelevant; the period is [2 pi] divided by the coeffcient of t; it comes out to pi/2 again.