Is it true that (if not true, give correct answer)

(a) for any positive integer k

(b) for a periodic signal x(t) of fundamental period T₀

for any value of t₀? Consider, for instance, x(t) =cos(2Ï€ t).

(c) cos(2Ï€ t) δ(t ˆ’ 1) = 1?

(d) if x(t) = cos(t) u(t) then d x(t)/dt = ˆ’sin(t) u(t) + δ(t) ?

(e) the integral

(f) if x(t) = cosh(t) u(t) = 0.5 (e^t + e^ˆ’t) u(t) is d x(t)/dt = sinh(t) u(t) + δ(t)?

(g) that the power of the causal full-rectified signal x(t) = ˆ£sin(t)ˆ£ u(t) is twice the power of its even component x_e (t) = 0.5[x (t) + x(ˆ’t)]?

Transcribed Image Text:

}2лt dt = 0? To • Lo+To x(t)dt = x(t)dt to