The necessities in Random Processes

Single Random Variables

 * Random Variables ([[Media:RV1.RVariable.1.A.20200427.pdf |A.pdf]])
 * Distribution Function ([[Media:RV1.Distribution.2.A.201200428.pdf |A.pdf]])
 * Density Function ([[Media:RV1.Density.3.A.20200429.pdf |A.pdf]])
 * Functions of Random Variables ([[Media:RV1.RVFunction.4.A.20220317.pdf |A.pdf]])
 * Gaussian Random Variables ([[Media:RV1.4.Gaussian.20200430.pdf |A.pdf]], [[Media:RV1.4B.Gaussian.20180314.pdf |B.pdf]])
 * Other Distribution and Density Functions ([[Media:RV1.5.Other.20200501.pdf |A.pdf]])
 * Conditional Distribution and Density Functions ([[Media:RV1.6.Conditional.20200506.pdf |A.pdf]])

The Characteristics of a Single Random Variable

 * Expected Value ([[Media:RV2.Expectation.1.A.20200506.pdf |A.pdf]])
 * Moments ([[Media:RV2.Moment.2.B.20200507.pdf |A.pdf]], [[Media:RV2.Moment.2.B.20180320.pdf |B.pdf]])
 * Moment Generating Functions ([[Media:RV2.MFunctions.3.A.20200508.pdf |A.pdf]])
 * Transformations of Random Variables ([[Media:RV2.Transform.4.A.20200514.pdf |A.pdf]])

Multiple Random Variables

 * Vector Random Variables ([[Media:3MRV.1A.VectorRV.20200515.pdf |A.pdf]])
 * Joint Distribution ([[Media:3MRV.2A.JointDist.20200518.pdf |A.pdf]])
 * Joint Density ([[Media:3MRV.3A.JointDensity.20200521.pdf |A.pdf]])
 * Conditional Joint Distribution and Density ([[Media:3MRV.4A.CondDistrib.20200527.pdf |A.pdf]])
 * Statistical Independence ([[Media:3MRV.5A.StatIndep.20200423.pdf |A.pdf]])
 * Sums of Random Variables ([[Media:3MRV.6A.RVSum.20200528.pdf |A.pdf]])
 * Central Limit Theorem ([[Media:3MRV.7A.CLimit.20200612.pdf |A.pdf]])

The Characteristics of Multiple Random Variables

 * Expected Values ([[Media:4MRV.1A.Expect.20200617.pdf |A.pdf]])
 * Joint Characteristic Functions ([[Media:4MRV.2A.JChar.20200618.pdf |A.pdf]])
 * Jointly Gaussian Random Variables ([[Media:4MRV.3A.JGauss.20200619.pdf |A.pdf]])
 * Transformations of Multiple Random Variables ([[Media:4MRV.4A.Transform.20200620.pdf |A.pdf]])
 * Linear Transformation of Gaussian Random Variables ([[Media:4MRV.5A.LinearTrans.20200623.pdf |A.pdf]])
 * Simulating Multiple Random Variables ([[Media:4MRV.6A.Simulation.20200624.pdf |A.pdf]])
 * Sampling and Some Limit Theorem ([[Media:4MRV.7A.LimitTheorem.20200625.pdf |A.pdf]])
 * Complex Random Variables ([[Media:4MRV.8A.ComplexRV.20200626.pdf |A.pdf]])

The Temporal Characteristics of Random Processes

 * Random Processes ([[Media:5MRV.1A.RandomProcess.20230419.pdf |A.pdf]], [[Media:5MRV.1B.RPBackground.20240325.pdf |B.pdf]], [[Media:5MRV.1C.RPBackground.20240709.pdf |C.pdf]])
 * Joint Distribution, Independence, Processes ([[Media:5MRV.2A.JointDistribution.20221012.pdf |A.pdf]])
 * Stationary Random Processes ([[Media:5MRV.3A.Stationary.20220402.pdf |A.pdf]], [[Media:5MRV.3B.Stationary.20221011.pdf |B.pdf]])
 * Covariance & Correlation of Random Variables ([[Media:5MRV.4A.CovCorrRV.20210910.pdf |A.pdf]])
 * Covariance & Correlation of Random Processses ([[Media:5MRV.5A.CovCorrRP.20210911.pdf |A.pdf]])
 * Example Random Processes ([[Media:5MRV.4A.Example.20210227.pdf |A.pdf]])
 * Ergodic Random Processes ([[Media:5MRV.5A.Ergodicity.20211022.pdf |A.pdf]], [[Media:5MRV.7B.Ergodicity.20211215.pdf |B.pdf]])
 * Measurement of Correlation Functions ([[Media:5MRV.6A.Measure.20201013.pdf |A.pdf]])
 * Complex Random Processes ([[Media:5MRV.7A.Complex.20201022.pdf |A.pdf]])

The Spectral Characteristics of Random Processes

 * Power Density Spectrum - Continuous Time ([[Media:6MRV.1A.PSpecCT.20210204.pdf |A.pdf]])
 * Auto Correlation Function ([[Media:6MRV.2A.AutoCor.20201218.pdf |A.pdf]])
 * Power Density Spectrum - Discrete Time ([[Media:6MRV.3A.PSpecDT.20201203.pdf |A.pdf]])
 * Cross Power Density Spectrum ([[Media:6MRV.4A.CPSpec.20191108.pdf |A.pdf]])
 * Cross Correlation Function ([[Media:6MRV.5A.CCorrel.20191114.pdf |A.pdf]])
 * Noise Definitions ([[Media:6MRV.6A.Noise.20191121.pdf |A.pdf]])
 * Power Spectrum of Complex Random Processes ([[Media:6MRV.7A.ComplexProc.20191125.pdf |A.pdf]])

Linear System with Random Inputs

 * Continuous Time LTI System ([[Media:7LTI.1A.CTime.20191203.pdf |A.pdf]])
 * Discrete Time LTI System ([[Media:7LTI.2A.DTime.20191211.pdf |A.pdf]])
 * System Response ([[Media:7LTI.3A.Response.20191224.pdf |A.pdf]])
 * Spectral Characteristics ([[Media:7LTI.4A.Spectral.20200104.pdf |A.pdf]])
 * Noise Modeling ([[Media:7LTI.5A.Noise.20200122.pdf |A.pdf]])

Optimum Linear System

 * Maximum SNR ([[Media:8OPT.1A.MaxSNR.20200128.pdf |A.pdf]])
 * Minimum Squared Error ([[Media:8OPT.2A.MinSE.20200207.pdf |A.pdf]])

Noise in Some Application Systems

 * AM Communication Systems ([[Media:9APP.1A.AM.20200212.pdf |A.pdf]])
 * FM Communication Systems ([[Media:9APP.2A.FM.20200221.pdf |A.pdf]])
 * Control Systems ([[Media:9APP.3A.Control.20200225.pdf |A.pdf]])
 * PLL Systems ([[Media:9APP.4A.PLL.20200305.pdf |A.pdf]])
 * Random Waveforms ([[Media:9APP.5A.RandWave.20200311.pdf |A.pdf]])
 * Radar Systems ([[Media:9APP.6A.Radar.20200313.pdf |A.pdf]])

Correlation and Power Spectra

 * 1) Correlation Functions of Random Signals ([[Media:RAND.1.A.Correlation.20121106.pdf |pdf]])
 * 2) Spectra of Random Signals ([[Media:RAND.2.A.Spectra.20121108.pdf |pdf]])

Random Processes and Linear Systems

 * 1) Time Domain Techniques for Noisy Signals ([[Media:RAND.3.A.Time.20130205.pdf |A.pdf]], [[Media:Dirichlet.pdf |B.pdf]])
 * 2) Frequency Domain Techniques for Noisy Signals
 * 3) Correlation v.s. Convolution for Noisy Signals

go to [ Electrical_%26_Computer_Engineering_Studies ]
 * 1) System Identification ([[Media:RP.SysId.1.A.pdf |pdf]])
 * 2) Matched Filter