Correlation and Convolution

Correlation and Convolution

Relation

s (τ) ⋆ g (τ) = s^{*} (- τ) * g (τ)

s^{*} (τ) * g (τ) = s (- τ) ⋆ g (τ)

Feature comparison

	convolution	correlation
commutativity	Y	N
	$s (t) * h (t) = h (t) * s (t)$	$φ_{s g} (τ) = φ_{g s}^{*} (- τ)$
associativity	Y	N
	$f (t) * (s (t) * h (t)) = (f (t) * s (t)) * h (t)$	Not equal
distributivity	Y	N?
	$f (t) * (s (t) + h (t)) = f (t) * s (t) + f * h (t)$	...