Overview

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Delve into an extensive lecture series covering advanced topics in signals and systems, including probability theory, random variables, stochastic processes, and signal processing. Begin with a review of probability fundamentals and progress through conditional probability, Bayes' rule, and random variables. Explore parameter estimation, linear programming, and optimization techniques. Examine discrete stochastic processes, Markov chains, and their applications. Study Poisson processes, deterministic and stochastic modeling, and various signal representations. Analyze wide-sense stationary processes, Gaussian processes, and their properties. Investigate power spectral density, Hilbert transforms, and bandpass signal representation. Conclude with an in-depth look at in-phase and quadrature components of bandpass processes and their spectral densities.

Syllabus

EE 306 - Signals and Systems II - Lecture 1 - Review of Probability Fundamentals.
EE 306 - Signals and Systems II - Lecture 2 - Conditional Probability, Bayes Rule and Independence.
EE 306 - Signals and Systems II - Lecture 3 - Review of Random Variables.
EE 306 - Signals and Systems II - Lecture 4 - Functions of Random Variables and Transform Methods.
EE 306 - Signals and Systems II - Lecture 5 - Probability Bounds and Recursion.
EE 306 - Signals and Systems II - Lecture 6 - Pairs of Random Variables.
EE 306 - Signals and Systems II - Lecture 7 - Covariance, Correlation Coefficent, Functions of Pairs.
EE 306 - Signals and Systems II - Lecture 8 - Vectors of Random Variables, Sum of Random Variables.
EE 306 - Signals and Systems II - Lecture 9 - Parameter Estimation, Linear MMSE Estimator.
EE306 - Signals and Systems II - Lect. 10 - Linear MMSE Estimator for Vectors, Generalized MMSE Est..
EE 306 - Signals and Systems II - Lecture 11 - Linear Programming and Duality in Optimization.
EE 306 - Signals and Systems II - Lecture 12 - Lagrange Dual Problem, Descent Methods.
EE 306 - Signals and Systems II - Lect. 13 - Discrete Stochastic Processes & Intro. to Markov Chains.
EE 306 - Signals and Systems II - Lecture 14 - n-step Transition Probabilities.
EE 306 - Signals and Systems II - Lecture 15 - 2 Umbrella Problem and Random Walk.
EE 306 - Signals and Systems II - Lecture 16 - Classification of States.
EE 306 - Signals and Systems II - Lecture 17 - Several Examples for Classification of States.
EE 306 - Signals and Systems II - Lecture 18 - Steady State Probabilities and Long Term Averages.
EE 306 - Signals and Systems II - Lec. 19-1 - Birth-Death Chains, Mean First Passage & Recurrence T..
EE 306 - Signals and Systems II - Lec. 19-2 - Example for Mean First Passage & Recurrence Times.
EE 306 - Signals and Systems II - Lecture 20 - Exponential Random Variable.
EE 306 - Signals and Systems II - Lecture 21 - Counting Processes.
EE306 - Signals and Systems II - Lec. 22 - Poisson Process, Properties & Moment Generating Functions.
EE 306 - Signals and Systems II - Lecture 23 - Poisson Processes Continued.
EE 306 - Signals and Systems II - Lecture 24 - Splitting and Merging Poisson Processes.
EE306 - Signals and Systems II - Lec. 25 - A Long Ex. Related to Poisson Process - Bus Departure Ex..
EE 306 - Signals and Systems II - Lecture 26 - Random Telegraph Signal and Shot Noise.
EE 306 - Signals and Systems II - Lecture 27 - Deterministic and Stochastic Modelling.
EE 306 - Signals and Systems II - Lecture 28 - Stochastic Modelling Continued.
EE 306 - Signals and Systems II - Lecture 29 - p.d.f Description of Random Phase Cosine Signal.
EE 306 - Signals and Systems II - Lecture 30 - Stationarity.
EE 306 - Signals and Systems II - Lecture 31 - Stationarity.
EE 306 - Signals and Systems II - Lecture 32 - Gaussian Processes.
EE 306 - Signals and Systems II - Lecture 33 - A Gaussian Processes Example & LTI Processing of WSS.
EE 306 - Signals and Systems II - Lecture 34 - Moment Char. of a Process for WSS Input & White Noise.
EE 306 - Signals and Systems II - Lec. 35 - Properties of Autocorrelation Function of WSS Processes.
EE 306 - Signals and Systems II - Lecture 36 - Power Spectral Density.
EE 306 - Signals and Systems II - Lecture 37 - Power Spectral Density Continued & Hilbert Transform.
EE 306 - Signals and Systems II - Lecture 38 - Bandpass Signal Representation.
EE 306 - Signals and Systems II - Lecture 39 - Representation of Bandpass Processes.
EE 306 - Signals and Systems II - Lecture 40 - In-phase & Quadrature (I/Q) Comp. of a Bandpass Proc..
EE 306 - Signals and Systems II - Lecture 41 - Spectral Density of I/Q Comp. of a Bandpass Process.