Why do we use convolution in LTI?

Convolution is an incredibly useful operation because it can be used to predict the output of an LTI system to any input. Then the convolution of x(t) and h(t) is the predicted output of the system (e.g. the firing rate in response to the arbirary visual stimulus).

Why do we use convolution of signals?

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. Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response.

What is convolution LTI?

It tells us how to predict the output of a linear, time-invariant system in response to any arbitrary input signal. The other (more common way) of interpreting the convolution sum is that it tells us that the output is computed by taking a weighted sum of the present and past input values.

Can convolution apply to non LTI?

The impulse response, h[n], and the convolution operation are DEFINED based on a system being LTI. Therefore they are in a strict sense only applicable to linear, time-invariant systems. However, you will still probably see them used even for systems that aren’t LTI.

What is meant by LTI system?

In system analysis, among other fields of study, a linear time-invariant system (LTI system) is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below.

What is convolution of a function?

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.