EEEM019

Random Processes, Lecturer JI
Hours 10 lecture hours + 2 problem classes

[1-2] Probability - Interpretation of probability. Sample spaces and events. Axioms of probability. Joint and conditional probability. Bayes' formula. Independent events.

[3-4] The Random Variable - Discrete and continuous random variables. Distribution and density functions. Moments of a random variable. Gaussian random variables. Other continuous and discrete distributions.

[5] Jointly Distributed Random Variables - Joint, marginal, and conditional distributions. Bivariate distributions. Statistical independence. Covariance and correlation coefficient. Jointly Gaussian random variables.

[6-7] Random Processes - Probability distributions. Time and ensemble averages. Stationarity and ergodicity. Correlation functions. Power spectral densities of random signals. Wiener- Khinchine theorem. Markov processes. Nonlinear and non-Gaussian processes.

[8] Linear Systems with Random Inputs - Mean, autocorrelation, and power spectral density of the output. Cross correlation function of input and output.

[11-12] Statistical Computing - Random numbers, meaning and generation. Computer modelling of random vectors. Monte Carlo methods. Reduction of variance.

[10] Revision

Signal Analysis, Lecturer SW
Hours 9 lecture hours + 2 Problem Classes

[1-2] Signal Representation and Time Domain Analysis - Review of basic signal functions, Dirac Delta functions, Time scaling, shifting and reversal, linear and circular convolutions, auto and cross correlations, properties of correlation, signal power/energy.

[3-4] Frequency Domain Analysis - Continuous time Fourier Transform, Properties of Fourier Transforms, Parseval’s Theorem, Frequency selective filtering, Sampling theory and practical limitations (Nyquist rate), Quantisation.

[5-9] Discrete Signal Transforms - Discrete Fourier Transform, Fast Fourier Transform, z-Transform, ROC, Properties of z-Transforms, Inverse z-Transforms.

Digital Signals and Systems, Lecturer SW
Hours 9 Lecture hours + 2 Problem Classes

[1-3] General Digital System Properties - Causality, Conditions of causality, Real systems, Stability, Conditions of stability, Pole-zero representations of Digital Systems, System Frequency Response, General Difference Equation, Transfer Function, Phase response, Magnitude response, Relationship between Impulse response and Frequency response.