Signals & Systems II: Complex Random Vectors and Stationarity

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Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Probability and Stochastic Processes: Fundamentals and Applications

Discusses the fundamentals of probability and stochastic processes, focusing on random variables, their properties, and applications in statistical signal processing.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Hermitian Spaces: Theory and Applications

Explores the theory of Hermitian spaces and their applications in quadratic forms and codimension 1 spaces.

Theory of MCMC

Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.

Explores correlated sampling, weight functions, Markovian chains, ergodicity, and walkers.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Stochastic Processes: 2nd Order Analysis

Explores stochastic processes, stationarity, ergodicity, and Wiener filtering for image restoration.

Stochastic Processes: Second Order Analysis

Covers the analysis of second-order stochastic processes in communication systems and image restoration using the Wiener filter.

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.