5.3.2. Suppose X(t) is WSS and second order ergodic with mean µX = 1 and autocorrelation
RX(τ )= 2 tri(4τ ). Further suppose Y (t) = 2X(t) + A, where E[A] = 1, E[A2
] = 2, and A
is independent of X(t) for all t.
(a) Determine PX and SX(f).
(b) Determine RY (τ ). Hint: Find E[Y (t + τ )Y (t)].
(c) Determine PY and SY (f).
(d) Determine RX,Y (τ ). Hint: Find E[X(t + τ )Y (t)].
(e) Determine SX,Y (f).
![5.3.2. Suppose X(t) is WSS and second order ergodic with mean µX = 1 and autocorrelation RX(τ )= 2 tri(4τ ). Further suppose Y (t) = 2X(t) + A, where E[A] = 1, E[A2 ] = 2, and A is independent of X(t) for all t. (a) Determine PX and SX(f). (b) Determine RY (τ ). Hint: Find E[Y (t + τ )Y (t)]. (c) Determine PY and SY (f). (d) Determine RX,Y (τ ). Hint: Find E[X(t + τ )Y (t)]. (e) Determine SX,Y (f).](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/08/532.png?w=1170&ssl=1 "5.3.2. Suppose X(t) is WSS and second order ergodic with mean µX = 1 and autocorrelation RX(τ )= 2 tri(4τ ). Further suppose Y (t) = 2X(t) + A, where E[A] = 1, E[A2 ] = 2, and A is independent of X(t) for all t. (a) Determine PX and SX(f). (b) Determine RY (τ ). Hint: Find E[Y (t + τ )Y (t)]. (c) Determine PY and SY (f). (d) Determine RX,Y (τ ). Hint: Find E[X(t + τ )Y (t)]. (e) Determine SX,Y (f).")
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