Consider the complex-valued signal x(t) = 1-jt/2+jt . Determine Re{x(t)}, Im{x(t)}, |x(t)|, and
Suppose x[n] = sqrt(3) + j if n <= 3 1 - j if -2 <= n <= 2 3j if n >= 3 and y[n] = 2e jpi/6 if n <= 2 2sqrt(2)e -jpi/4 if 3 <= n <= 6 nejpi/2 if n >= 7 . Determine |x[n]|,
Suppose x(t) = sqrt(5)t^2(u(t) - u(t - 2)) and y[n] = del[n] - 2del[n - 1] + del[n - 4] + 2del[n - 7]. Determine the energy of these signals, Ex and Ey.
Suppose x(t) is periodic with fundamental period T0 = 10 and fundamental cycle x(t) = -(u(t + 5) - u(t + 2)) + 2(u(t + 2) - u(t - 3)) - (u(t - 3) - u(t - 5)). Also suppose y[n] is periodic with fundamental period N0 = 6 and fundamental cycle y[n] = 3del[n + 3] + 2del[n + 2] + del[n + 1] - del[n] - 2del[n - 1] - 3del[n - 2]. Determine the power of these signals, Px and Py.
Consider the aperiodic signals x(t) = t(u(t)-u(t-4))+4u(t-4) and y[n] = (1/2)^n if n >= 0 2 if n <= -1 . Determine the power of these signals, Px and Py.
Suppose x(t) = (1 + t)(u(t) - u(t - 1)) and y(t) = (1 - t)(u(t) - u(t - 1)). Determine the correlation Rx,y, the correlation coefficient (rho)x,y, and the mean-square error MSEx,y.
Suppose x[n] = del[n] + 2del[n - 1] + 3del[n - 2] + 4del[n - 3] and y[n] = -4del[n] - 3del[n - 1] - 2del[n - 2] - del[n - 3]. Determine the correlation Rx,y, the correlation coefficient (rho)x,y, and the mean-square error MSEx,y.
Suppose x(t) and y(t) are periodic with fundamental period T0 = 4 and fundamental cycles x(t) = (u(t) - u(t - 2)) and y(t) = t(u(t + 2) - u(t - 2)). Determine the correlation Rx,y, the correlation coefficient (rho)x,y, and the mean-square error MSEx,y.
Suppose x[n] and y[n] are periodic with fundamental period N0 = 5 and fundamental cycles x[n] = 3del[n + 2] + 2del[n + 1] + 1del[n - 2] and y[n] = -3del[n + 2] - 2del[n - 1] - 1del[n - 2]. Determine the correlation Rx,y, the correlation coefficient (rho)x,y, and the mean-square error MSEx,y.