===Translation invariance===The convolution commutes with translations, meaning that:formula_41where τ"x"f is the translation of the function "f" by "x" defined by:formula_42If "f" is a Schwartz function, then τ"x""f" is the convolution with a translated Dirac delta function τ"x""f" = "f"∗"τ""x" "δ".
=== Translation invariance ===The convolution commutes with translations, meaning that:formula_36where τ"x"ƒ is the translation of the function ƒ by "x" defined by:formula_37If ƒ is a Schwartz function, then τ"x"ƒ is the convolution with a translated Dirac delta function τ"x"ƒ = ƒ∗τ"x" δ.