Question

Autocorrelation and cross correlation formula

Answer 1

what is zeeman effect?

Answer 2

AUTOCORRELATION FUNCTION
Consider a time-limited (or band-limited) signal x(t),
x(t) =
x(t), 0 ≤ t ≤ T,
0, otherwise; (A.1)
its autocorrelation function is defined as
Cxx(t, t + τ) = E[x(t)x(t + τ)]
≈ 1
T
-
T
0
x(t)x(t + τ)dt, (A.2)
where the definition equation in the first line is specified for random signals whereas
the second line is more general and also applicable for deterministic signals. If the
random signal x(t) is drawn from an ergodic stochastic process, then the ensemble
average can be approximated by the time average by allowing the duration T to
approach infinity.
Some important concepts and properties related to the autocorrelation are sum-
marized here:
• If x(t) is drawn from a wide-sense stationary process, then its autocorrelation
function is shift invariant, namely,
Cxx (t, t + τ) = Cxx(τ). (A.3)
Correlative Learning: A Basis for Brain and Adaptive Systems, by Zhe Chen, Simon Haykin,
Jos J. Eggermont, and Suzanna Becker
Copyright 2007 John Wiley & Sons, Inc.