Ch.1 Basic Descriptions and Properties

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Presentation transcript:

Ch.1 Basic Descriptions and Properties D : deterministic data ND : non-deterministic (random) explicit mathematical relationship 실험적으로 data 재현 가능 m x(t)

Ch.1 Basic Descriptions and Properties Periodic Sinusoidal : Complex Periodic : 삼각파, 사각파  Fourier Series Amplitude

Ch.1 Basic Descriptions and Properties Nonperiodic Almost periodic : 무리수 등간격이 안됨 Transient

Ch.1 Basic Descriptions and Properties Nondeterministic (random) Stationary Ergodic Nonergodic Nonstationary 1) ensemble averaging xN(t) x2(t) x1(t) sample fn ensemble averaging random process

Ch.1 Basic Descriptions and Properties ※ (weakly) stationary의 성질 : mean of random process ( 에 무관) : autocorrelation all possible moments and joint moment are time invariant  strongly stationary 2) time averaging 가 sample fn 에 따라 불변 + Stationary  Ergodic All other properties도 만족 ensemble/time 모두 Averaging하면 증명됨 * 여기서 다룰 data  모두 ergodic

Ch.1 Basic Descriptions and Properties Analysis of Random Data Single stationary random data mean, variance p.d.f auotocorrelation autospectral (표현하는 중요한 확률적 성질) Pairs of random record Joint p.d.f Cross-correlation function Cross-spectral density function FRF Coherence function I/O Relations Single-Input / Single-Output model (SISO) Single-Input / Multiple-Output model (SIMO) Multiple-Input / Single-Output model (MISO) Multiple-Input / Multiple-Output model (MIMO) superposition superposition

Ch.1 Basic Descriptions and Properties Statistical Error Variance Bias MSE (mean square error) variance error bias error MSE