Let the sequence (ph)hez be given as 1. h = 0 0.4, h = ±1 Ph= -0.8, h= ±2 0, |h| ≥ 3 a) Is ph the autocorrelation function of a stationary stochastic process? b) If yes, is such a process ergodic for the estimation of the expectation value? c) Let Ph now be defined as before but with p-2 = P2 = 0. Is the sequence now the autocor- relation function of a stationary stochastic process? If yes, is such a process ergodic for the estimation of the expectation value?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Let the sequence (ph)hez be given as
1.
h = 0
0.4,
h = ±1
Ph=
-0.8,
h = ±2
0,
|h| ≥ 3
a) Is ph the autocorrelation function of a stationary stochastic process?
b) If yes, is such a process ergodic for the estimation of the expectation value?
c) Let Ph now be defined as before but with p 2 = P2 = 0. Is the sequence now the autocor-
relation function of a stationary stochastic process? If yes, is such a process ergodic for the
estimation of the expectation value?
Transcribed Image Text:Let the sequence (ph)hez be given as 1. h = 0 0.4, h = ±1 Ph= -0.8, h = ±2 0, |h| ≥ 3 a) Is ph the autocorrelation function of a stationary stochastic process? b) If yes, is such a process ergodic for the estimation of the expectation value? c) Let Ph now be defined as before but with p 2 = P2 = 0. Is the sequence now the autocor- relation function of a stationary stochastic process? If yes, is such a process ergodic for the estimation of the expectation value?
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