<Dd> = ∫ R n f (x) e − 2 π i x ⋅ ν (∫ R n g (y) e − 2 π i y ⋅ ν d y) d x (\ displaystyle = \ int _ (\ mathbb (R) ^ (n)) f (x) e ^ (- 2 \ pi ix \ cdot \ nu) \ left (\ int _ (\ mathbb (R) ^ (n)) g (y) e ^ (- 2 \ pi iy \ cdot \ nu) \, dy \ right) \, dx) </Dd> <Dl> <Dd> <Dl> <Dd> <Dl> <Dd> = ∫ R n f (x) e − 2 π i x ⋅ ν d x ∫ R n g (y) e − 2 π i y ⋅ ν d y . (\ displaystyle = \ int _ (\ mathbb (R) ^ (n)) f (x) e ^ (- 2 \ pi ix \ cdot \ nu) \, dx \ int _ (\ mathbb (R) ^ (n)) g (y) e ^ (- 2 \ pi iy \ cdot \ nu) \, dy .) </Dd> </Dl> </Dd> </Dl> </Dd> </Dl> <Dd> <Dl> <Dd> <Dl> <Dd> = ∫ R n f (x) e − 2 π i x ⋅ ν d x ∫ R n g (y) e − 2 π i y ⋅ ν d y . (\ displaystyle = \ int _ (\ mathbb (R) ^ (n)) f (x) e ^ (- 2 \ pi ix \ cdot \ nu) \, dx \ int _ (\ mathbb (R) ^ (n)) g (y) e ^ (- 2 \ pi iy \ cdot \ nu) \, dy .) </Dd> </Dl> </Dd> </Dl> </Dd> <Dl> <Dd> <Dl> <Dd> = ∫ R n f (x) e − 2 π i x ⋅ ν d x ∫ R n g (y) e − 2 π i y ⋅ ν d y . (\ displaystyle = \ int _ (\ mathbb (R) ^ (n)) f (x) e ^ (- 2 \ pi ix \ cdot \ nu) \, dx \ int _ (\ mathbb (R) ^ (n)) g (y) e ^ (- 2 \ pi iy \ cdot \ nu) \, dy .) </Dd> </Dl> </Dd> </Dl>

Concept of convolution in time domain and frequency domain