Probabilistic methods in Electrical Engineering,
Building a Random Number Generator
Design Project
Have you ever wondered how your calculator or computer is able to generate random numbers. Ok, what generates these numbers is a specialize type of binary, digital, finite-state, feedback systems called pseudo-random number generators, or, simply, PN-Generators (see the figure below).
The reason these systems are called pseudo-random (not random) number generators is that: the sequences of numbers they emit are quite deterministic. It is just that they look random (to the unsuspecting observer). However, their properties and measures cannot be distinguished from those of a true random numbers. These systems are the basis for generating uniformly-distributed random variables, normally-distributed random variables, etc. PN-Generators have many other important applications in data transmission, multiplexing, and encryption.
The Project:
The aim of the project is to familiarize you with PN-Generators, and use them to generate two types of random variables having uniformly-distributed and normally distributed PDFs. The project is divided into two parts:
Part-1: in this part you have to read about these systems and understand how they work. I placed two good articles about this topic in the course WebCT project folder. However, your are strongly encouraged to search for more references about this subject. Your are required to submit a five to ten-page report containing technical details about the properties of these systems and how they work. You must also submit a power point presentation that expresses your understanding of the subject.
Part-2: Using the knowledge that you gained from the first part you must write a documented Matlab program that generates random variables for both specific uniform and normal PDFs. You must submit the program, and a short report, containing results verifying that the distribution of the variables is uniform and normal. You have till last day of classes to hand in this part.