EC2010 Probabilistic Analysis of Signals and Systems

The foundations of signals and systems are developed from probabilistic and statistical approaches. Emphasis is on signal processing, communication systems, and computer networks relevant to military applications. Topics include probability, random variables and random sequences; density and distribution functions; deterministic versus nondeterministic signals; expectation, the d.c. and the r.m.s. values of nondeterministic signals, correlation and covariance; radar and sonar signal detection; LTI systems, transformation of random variables and the central limit theorem; basic queuing theory and computer communication networks.

Prerequisite

EC2410 (may be concurrent)

Lecture Hours

3

Lab Hours

1

Course Learning Outcomes

• Given the description of a random experiment, the student will be able to determine the sample space, define events, and assign probability values.
• Given the conditional probabilities representing a binary communications channel (symmetric or asymmetric), the student will be able to determine the inverse probabilities and error probabilities including the total symbol error probability for binary and ternary representations.
• The student will be able to write the mathematical expressions and draw the plots of probability density functions of commonly used random variables, such as Bernoulli, binomial, geometric, Poisson, uniform, exponential, and Gaussian.
• Given the probability density function of a single random variable or a joint density function of two random variables, the student will be able to determine the first moment, the second moment, the second central moment, and cross moments.
• Given a set of independent and identically distributed random variables (i.e., having the knowledge of their pdfs), the student will be able to apply the central limit theorem to determine the pdf of the sum of the random variables both analytically and numerically (using Matlab).
• Given a random process, the student will be able to determine if it is wide-sense stationary as well as ergodic in the mean and ergodic in correlation.
• Given the impulse response of an LTI system and the statistical description of the input process, the student will be able to determine the statistics of the output signal.
• Given the birth-death representation of a queuing system, the student will be able to determine the average number of jobs in the system and average time in the system (for M/M/1 and M/M/1/K).