The following problems relate to the symmetry of the signal:

(a) Consider a causal exponential x(t) = e^ˆ’t u(t).

        i. Plot x(t) and explain why it is called causal. Is x(t) an even or an odd signal?

        ii. Is it true that 0.5e^{ˆ’ˆ£tˆ£} is the even component of x(t)? Explain.

(b) Using Euler€™s identity x(t) = e^jt =cos(t) + jsin(t), find the even x_e(t) and the xodd x_o(t) components of x(t).

(c) A signal x(t) is known to be even, and not exactly zero for all time, explain why

(d)  Is it true that

for any signal x(t)?

Transcribed Image Text:

| x(t) sin(2,t)dt = 0 [x(t) + x(-t)] sin(2,t)dt = 0 %3D