ExamRP931116 - Midterm Exam of Stochastic Processes Nov 16...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Midterm Exam of Stochastic Processes Nov. 16, 2004 1. Let ( ) j t t ae = ω X be a random process, where a is a real constant and ω is a random variable with pdf ( ) f ϖ ω . Let ( ) ( ) ju u f e d ϖ ϖ ϖ- Φ = ω ω be the characteristic function of ω . (a) (10 points) Express the mean ( ) t η and autocorrelation 1 2 ( , ) R t t of ( ) t X in terms of ( ) Φ ω . (b) (4 points) Determine whether ( ) t X is a WSS process. 2. (15 points) Let ( ) t X be a WSS random process with autocorrelation ( ) R τ XX and ( ) t Y be the output of an linear time-invariant (LTI) system with input ( ) t X . Let the LTI system can be expressed by 3 ( ) 2 ( ) ( ) ( ) 2 ( ) t t t t t t + + = + Y Y Y X X (a) Find the system function ( ) H s of the LTI system. (b) Find the power spectral density ( ) S ϖ YY of ( ) t Y . (c) Find 2 { ( ) } E t Y . 3. (10 points) Assume that the random points i t , which represent the times that earthquakes ( o ) occur, are Poisson points. Let λ be the average number of...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

ExamRP931116 - Midterm Exam of Stochastic Processes Nov 16...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online