Is convolution distributive over multiplication?

1. Are convolutions distributive?
2. Is convolution commutative with multiplication?
3. Is convolution different from multiplication?
4. What are the properties of convolution?

Are convolutions distributive?

The operation of convolution is distributive over the operation of addition. That is, for all continuous time signals x1, x2, x3 the following relationship holds.

Is convolution commutative with multiplication?

but that follows from the fact that multiplication and convolution are separately commutative semigroup operations.

Is convolution different from multiplication?

Convolution, for discrete-time sequences, is equivalent to polynomial multiplication which is not the same as the term-by-term multiplication. Convolution also requires a lot more calculation: typically N2 multiplications for sequences of length N instead of the N multiplications of the term-by-term multiplication.

What are the properties of convolution?

, Convolution is a linear operator and, therefore, has a number of important properties including the commutative, associative, and distributive properties.