Explain the formula of convolution and convolution theorem

1. What is the formula of convolution theorem?
2. What is convolution explain?
3. What is convolution theorem used for?
4. What is convolution and explain its types?

What is the formula of convolution theorem?

2.10.

The convolution theorem (together with related theorems) is one of the most important results of Fourier theory which is that the convolution of two functions in real space is the same as the product of their respective Fourier transforms in Fourier space, i.e. f ( r ) ⊗ ⊗ g ( r ) ⇔ F ( k ) G ( k ) .

What is convolution explain?

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.

What is convolution theorem used for?

The Convolution Theorem is certainly useful in solving differential equations, but it can also help us solve integral equations, equations involving an integral of the unknown function, and integro-differential equations, those involving both a derivative and an integral of the unknown function.

What is convolution and explain its types?

Convolution is a mathematical tool for combining two signals to produce a third signal. In other words, the convolution can be defined as a mathematical operation that is used to express the relation between input and output an LTI system.