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

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

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

4. 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

5. 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

6. 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

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