Why unit impulse function is used to find impulse response of an LTI system? Hello i am working in digital image restoration field, recently i have studied concept of convolution, i studied that to find the impulse response/point-spread function of an LTI system, an unit impulse function is passed from the system and its output is considered as impulse response, My question is that, Why an unit impulse function is used to find the impulse response of any LTI system, what is the mathematical and practical reason behind it.
It is important to realize that due to the LTI property the response to an impulse $\delta(n)$ describes the system completely, because any input signal can be written as a weighted sum of shifted impulses:

$$x(n)=\sum_kx(k)\delta(n-k)\tag{1}$$

Let $\mathcal{T}\{\cdot\}$ denote the system operator, so the response to a shifted impulse is

$$\mathcal{T}\{\delta(n-k)\}=h(n-k)\tag{2}$$

From (1) and (2), due the linearity and the time- (shift-)invariance of the system, the response to any input signal $x(n)$ can be written as a weighted sum of responses to shifted impulses:

$$y(n)=\mathcal{T}\{x(n)\}=\sum_kx(k)\mathcal{T}\{\delta(n-k)\}=
\sum_kx(k)h(n-k)$$

This last equality is the convolution sum describing the input-output relation of a discrete LTI system.