Instantaneous Spectrum

A(f) = F A(t)

Auto or Power Spectrum

G_AA(f) = A(f) · A^*(f)

Frequency Response

Coherence

Impulse Response

h(t) = F ^-1H(f)

Cross Spectrum

G_AB(f) = A^*(f) · B(f)

G_BA(f) = A(f) · B^*(f)

Auto Correlation

R_AA(τ) = F ^-1G_AA(f)

Cross Correlation

R_AB(τ) = F ^-1G_AB(f)

Legend

A, B = Input channels A and B

(t) = A function of time

(f) = A function of frequency

^* = Complex Conjugate

F = Fourier Transform

F ^-1 = Inverse Fourier Transform

τ = Time Shift