Question on convolution

1. What is the main purpose of convolution?
2. What is convolution example?
3. Why LTI is used for convolution?

What is the main purpose of convolution?

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response.

What is convolution example?

The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures). For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 18 at DTFT § Properties.)

Why LTI is used for convolution?

The reason LTI systems are incredibly useful is because of a key fact: if you know the response of the system to an impulse, than you can calculate the response of the system to ANY input. This gives you an enormous amount of predictive power.