Signals and Systems

Consider a real signal x(t), -∞ < t <∞, such that x(t) = 0 for t <0, x(t) = 2 for 0 ≤ t < 1 and x(t) = 0 for t≥ 1. Let E[x(t)] = ∫_∞^[x(t)]^2dt. Which of the following options correctly represents the ratio, E[x(t)]/E[3...

Let x(t) = 10 cos(10.5Wt) be passed through an LTI system having impulse response h(t) = π (sin Wt / πt)^2 cos 10Wt. The output of the system is

Let x1(t) = u(t + 1.5) - u(t - 1.5) and x2(t) is shown in the figure below. For y(t) = x1 (t) * x2 (t), the $\int_{-\infty}^{\infty}y(t)dt$ is ________ (rounded off to the nearest integer).

Consider the signal $f(t) = 1 + 2 \cos(\pi t) + 3 \sin(\frac{2\pi}{3} t) + 4 \cos(\frac{\pi}{2} t + \frac{\pi}{4})$, where t is in seconds. Its fundamental time period, in seconds, is _________.