اهداف درس: هدف اصلی این درس آشنایی با فرآیندهای تصادفی و مشخصه های آماری آنها می باشد. تخمین مشخصه های آماری، هموارسازی، پیش گویی و نمایش یک فرآیند در حوزه فرکانس (طیف توان) از دیگر اهداف این درس می باشد.
مباحث درس: 1.Definition of Random Variable and Review of Probability Concepts.
2.Definition of Stochastic Processes and its General Concepts.
3.Statistical Characteristics of Random Variables in Different Orders.
4.Strict-Sense Stationary Process (SSS) and Wide-Sense Stationary Process (WSS)
5.Cyclostationary Process.
6.Auto Correlation Function Properties, Power Spectrum (Discrete-Time and Continues Time Processes).
7.Random Input Systems Analysis, Relationship Between Statistical Characteristics of Input and Output, Spectral Relativity of Input and Output of Linear Systems.
8.Ergodic Processes (Distribution Eng., Correlation Erg., Mean-Ergodic).
9. Special Processes Analysis and their Applications.
10.White Noise, Thermal Noise, Wiener Process, Poisson Process, Shot Noise, PAM, Telegraph Signal.
11.Detection of Deterministic Signals in White and Color Noise, Matched Filter, Hilbert Transform.
12.Narrowband Processes and Sampling Theory.
13.Karhunen-Loeve (KL) Expansion and Fourier series as an Special Case of KL.
14.Factorization and Innovations.
15.Mean Square Linear Estimation.
16.Regular and Predictable Process.
17.Smoothing (Discrete-Time and Continuous-Time Processes).
18.Prediction (Discrete-Time and Continuous-Time Processes).
19.Filtering and Prediction (Discrete-Time and Continuous-Time Processes).
20.Estimation of a Regular Stationary Signal in White Noise as a Special Case
