신호의 교차상관함수신호의 교차상관함수
Definition
Analog Signal
For an Energy Signal f∈L2(R), f⋆g defined as follows is called the cross-correlation function defined by f and g.
(f⋆g)(τ)=Rfg(τ):=∫−∞∞f(t)g(t+τ)dt
Here, f(t) is the conjugate complex number of f(t).
Digital Signal
The cross-correlation function of energy signal {xn}∈ℓ2 is defined as follows.
(x⋆y)[n]=Rxy(m):=n∈N∑xnyn+m
Explanation
According to the definition, the autocorrelation function Rf(τ) is a special case of the cross-correlation function when g=f.
The Fourier transform of the cross-correlation function is called the cross (energy) spectrum.
Sfg(ω):=∫−∞∞Rfg(τ)e−iτωdτ=R^fg(ω)
See Also
Stochastic Process