{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

wide_sense_stationary_processes

wide_sense_stationary_processes - 2.2 Wide-Sense...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
2.2. Wide-Sense Stationary (WSS) Processes Mean of the random process X ( t ) is the mean of random variable X ( t ) at time instant t . + = dx x xf t X E t X ) ( )] ( [ ) ( ) ( )] ( [ t t X E X μ = Let f X(t ) ( x ) be the pdf of X ( t ) at time instant t . Autocorrelation function of X ( t ) is a function of two variables t 1 = t and t 2 = t + τ , )] ( ) ( [ ) , ( τ τ + = + t X t X E t t R X This is a measure of the degree to which two time samples of the same random process are related
Image of page 1

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

View Full Document Right Arrow Icon
Autocorrelation function of X ( t ) is a function of two variables t 1 = t and t 2 = t + τ , )] ( ) ( [ ) , ( τ τ + = + t X t X E t t R X This is a measure of the degree to which two time samples of the same random process are related
Image of page 2
A random process X ( t ) is WSS if ) ( )] ( ) ( [ ) , ( ) ( constant )] ( [ ) ( ) ( τ τ τ μ X X X R t X t X E t t R ii t X E t i = = = = What is a WSS Process? In other words, a random process X ( t ) is WSS if its two statistics, its mean and autocorrelation, do not vary with a shift in the time origin.
Image of page 3

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

View Full Document Right Arrow Icon
Solution.
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern