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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 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:
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With this important detail, are there any significant differences with LSD?
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a) Is this an upper tail, lower tail, or two-tail test? b) Are we testing means or proportions? c) State the rule of rejection (in terms of p-value and level of significance)
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