Lecture19 - Motivation Lecture 19 Poisson and Gaussian...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
•1 Lecture 19 Poisson and Gaussian Processes Motivation Various applications invoke different random processes In signal processing and communications, the gaussian process is frequently used, e.g. gaussian channel, additive gaussian noise etc. In data networks, Poisson models are ubiquitous. ± Poisson processes: Many applications involve counting whose outcome is random Arriving customers or passengers at a check out counter, or at a station Counting the number of photons which hit a surface Definition: A random process is called a Poisson random process if the following properties are satisfied, )} , 0 [ ), ( { t t N 1. N(0)=0 w.p.1 2. is a process with IID increments. 3. For all t>s, the RV is Poisson distributed, i.e. its PMF is given by is a parameter we will refer to as a “rate”. )} ( { t N ) ( ) ( ) , ( s N t N s t I = ,... 2 , 1 , 0 ! )] ( [ ) ) , ( ( ) ( = = = k k s t e k s t I P k s t λ 0 >
Background image of page 1

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

View Full DocumentRight Arrow Icon
•2 ¾ Remark: describes and counts the “jumps” within The process statistics are concentrated at To find the probability that some number of jumps occur in a given time interval, we can use the above formula: ) , ( s t I ). , [ s t ). , [ s t t e t t t I P Δ = = Δ + λ ) 0 ) , ( ( t te t t t I P Δ
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/24/2009 for the course ECE 514 taught by Professor Krim during the Fall '08 term at N.C. State.

Page1 / 5

Lecture19 - Motivation Lecture 19 Poisson and Gaussian...

This preview shows document pages 1 - 3. Sign up to view the full document.

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