Introduction: Random input signals, random disturbances, random system characteristics, random experiments and events.
Random variables: Concept of random variable, distribution functions, density functions, mean values and moments, the Guassian random variable, density functions related to guassian- Rayleigh distribution, Maxwell distribution, Chi-square distribution, log normal distribution. Other distribution functions-uniform distribution, exponential distribution, delta distribution. Conditional probability distribution and density functions.
Several random variables: Two random variables, joint conditional probability, statistical independence, correlation between random variables, density function of the sum of two random variables, probability density function of a function of two random variables, thecharacteristic function.
Random Processes: Continuous and discrete, deterministic and nondeterministic, stationary and nonstationary, ergodic and nonergodic.
Correlation functions: Introduction, autocorrelation function of a binary process, properties of auto correlation functions, examples of autocorrelation functions, crosscorrelation functions, properties of crosscorrelation functions, examples and applications of crosscorrelation functions, correlation matrices for sampled functions.
Spectral Density: Introduction, relation of spectral density to the fourier transform, properties of spectral density, spectral density and the complex frequency plane, mean square values from spectral density, relation of spectral density to the autocorrelation function, white noise, cross spectral density, examples and applications of spectral density,
Response of linear systems to random input: Analysis in the time domain, mean and mean square value of system output, auto correlation function of system output, crosscorrelation between input and output, spectral density at the system output.
Optimum linear systems: Criteria of optimality, restrictions on the optimum system, optimization by parameter adjustment, systems that maximize signal-to-noise ratio, systems that minimize mean square error.
1. G. R. Cooper and C. D. Mcgillem: Probabilistic Methods of Signal and System Analysis, Third Edition, Oxford University Press.
2. M. Lefebvre: Applied Probability and Statistics, Springer, Macmillan India Limited.
3. A. Papoulis, S. U. Pillai: Probability, Random Variable and Stochastic Processes, TMH.