Lectures related to Signals & Systems II: Complex Random Vectors and Stationarity

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Signals & Systems II: Second Order Statistics

Explores second order statistics in signal processing, stationarity in random signals, and the distinction between ergodic and non-ergodic processes.

Estimation and Linear Prediction - Part 2

Explores power spectral density, Wiener-Khintchine theorem, ergodicity, and correlation estimation in random signals for signal processing.

Stationarity in Stochastic Processes

Explores stationarity in stochastic processes, showcasing how statistical characteristics remain constant over time and the implications on random variables and Fourier transforms.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Continuous-Time Stochastic Processes: Ergodicism Examples

Introduces continuous-time stochastic processes and provides examples illustrating ergodicism.

Elliptical Distributions: Properties and Applications

Covers elliptical distributions, including properties, applications, and risk management implications.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Stochastic Processes: Basics & Stationarity

Covers signal generation, statistical relations, stationarity, white noise, and orthogonality in stochastic processes.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Gaussian Random Vectors

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Elements of Statistics: Memorylessness, Stationary Processes, Estimation using MLE

Explores memorylessness in distributions, stationary processes, and estimation using MLE.

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Stochastic Models for Communications

Covers stochastic models for communications, including stationarity, ergodicity, power spectral density, and Wiener filter.

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.