An important concept in many communications applications is the correlation between two signals. Let x(t) and y(t) be two signals; then the correlation function is defined as y(t) = _*_*_x(t+1)y(1)dt The function $x<(t) is usually referred to as the auto-correlation function of the signal x(t), while oxy(t) is often called a cross-correlation function. 1) What is the relationship between oxy(t) and 2) Suppose that y(t) = x(t +T). Express oxy(t) and (t)? (t) in terms of Ox(t).

In an continuous LTI system, for input u(t), the output is 2(1 - e)u(t); for input cost, the output is √2 cos(t-4). Find the output y(t) for the following input: (a) x(t) = 2u(t) - 2u(t-1) (b) x(t) = 4 cos(2(t-2)) (c) x(t) = 5u(t) + 10 cos(10t)