In Problem 10.12.1, we found that passing a stationary white noise process through an integrator produced a nonstationary output process Y(t). Does this example violate Theorem 11.2?
Problem 10.12.1
A white Gaussian noise process N(t) with autocorrelation RN (τ ) = αδ(τ ) is passed through an integrator yielding the output
Find E[Y(t)] and the autocorrelation function RY (t,τ). Show that Y(t) is a nonstationary process.
Theorem 11.2
If the input to an LTI filter with impulse response h(t) is a wide sense stationary process X(t), the output Y (t) has the following properties:
