Convolution theorem formula

(f∗g)(t)=∫t0f(t−u)g(u)du.

1. How do you use convolution theorem?
2. What is convolution theorem in mathematics?
3. How do you prove the convolution theorem?

How do you use convolution theorem?

One use of the Laplace convolution theorem is to provide a pathway toward the evaluation of the inverse transform of a product in the case that and are individually recognizable as the transforms of known functions.

What is convolution theorem in mathematics?

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function ( ) that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it.

How do you prove the convolution theorem?

Proof of the convolution theorem

Note, in the equation below, that the convolution integral is taken over the variable x to give a function of u. The Fourier transform then involves an integral over the variable u. Now we substitute a new variable w for u-x. As above, the infinite integration limits don't change.