An integrator produced a nonstationary output process

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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 R_N (τ ) = αδ(τ ) is passed through an integrator yielding the output

Find E[Y(t)] and the autocorrelation function R_Y (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:

Reference no: EM131083379

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