{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

630F09_hw5 - ENEE 630 Fall 2009 Homework#5 Problem 1 A rst...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ENEE 630 Fall 2009 Homework #5 Problem 1 A first order autoregressive (AR) process { u(n) } that is real-valued satisfies the real-valued difference equation u ( n ) + a 1 u ( n - 1) = v ( n ) where a 1 is a constant and { v(n) } is a white-noise process of varance σ 2 v . Such a process is also referred to as a first-order Markov process . (a) Suppose in practical implementation, the generation of the process { u(n) } starts at n=1 with initialization u(0)=0. Determine the mean of the actual { u(n) } process that we have obtained. Under what conditions E [ u ( n )] converges to a constant and what the constant is? (b) Now consider the case when { v(n) } has zero mean. Determine the variance of the actual { u(n) } process that we have obtained. Under what conditions V ar [ u ( n )] converges to a constant and what the constant is? (c) For the conditions specified in part (b), find the autocorrelation function of the AR process { u(n) } . Sketch this autocorrelation function for the two cases 0 < a 1 < 1 and - 1 < a 1 < 0.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}