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01Terminology - Continuous time system analog Discrete time...

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MAE 591 RANDOM DATA: ANALYSIS AND PROCESSING (3:1:3) Fall Semester, 2002 Mechanical Engineering Department, KAIST Terminology Time history record : Deterministic : Accurately predicted in detail; repeatable ; trends Random : Not accurately predicted in detail; not repeatable ; errors Ensemble : Collection of all time history records (sample functions), x t i i ( ), , , , = ⋅⋅⋅ 1 2 3 Defines a random process , { } x t ( ) Transient Steady state Continuous system = Distributed parameter system = Infinite degree-of-freedom system ; PDE Discrete system = Lumped parameter system = Multi-degree-of-freedom system ; ODE
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Unformatted text preview: Continuous time system : analog Discrete time system : sampling; digital Stationary process : Probability distributions are invariant under a shift of the time scale Strongly stationary Weakly stationary : first and second order probability distributions are invariant. Nonstationary process Locally stationary : ) ( ) ( ) , ( 2 1 τ R t R t R = Ergodic process : Ensemble averages = Temporal averages Almost all stationary processes are ergodic Strongly ergodic Weakly ergodic Non-ergodic process...
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