<Dd> G (ν) = F (g) = ∫ R n g (x) e − 2 π i x ⋅ ν d x, (\ displaystyle G (\ nu) = (\ mathcal (F)) \ (g \) = \ int _ (\ mathbb (R) ^ (n)) g (x) e ^ (- 2 \ pi ix \ cdot \ nu) \, \ mathrm (d) x,) </Dd> <P> where the dot between x and ν indicates the inner product of R. Let h (\ displaystyle h) be the convolution of f (\ displaystyle f) and g (\ displaystyle g) </P> <Dl> <Dd> h (z) = ∫ R n f (x) g (z − x) d x . (\ displaystyle h (z) = \ int \ limits _ (\ mathbb (R) ^ (n)) f (x) g (z-x) \, \ mathrm (d) x .) </Dd> </Dl> <Dd> h (z) = ∫ R n f (x) g (z − x) d x . (\ displaystyle h (z) = \ int \ limits _ (\ mathbb (R) ^ (n)) f (x) g (z-x) \, \ mathrm (d) x .) </Dd>

Convolution in the time domain is multiplication in the frequency domain