Why only impulse signal for convolution?

1. Why is impulse response required for convolution?
2. Why do we use impulse signal?
3. What is the convolution of signal with an impulse?
4. Why convolution is applicable on LTI systems only?

Why is impulse response required for convolution?

The impulse response function is a useful transfer characteristic of a signal processing unit, since it allows us to estimate the expected distortion of a signal passing through it. Convolution.

Why do we use impulse signal?

The impulse response can be used to find a system's spectrum. Here is the rationale: if the input signal in the frequency domain is a constant across all frequencies, the output frequencies show how the system modifies signals as a function of frequency.

What is the convolution of signal with an impulse?

Convolution with an impulse: sifting and convolution

Another important property of the impulse is that convolution of a function with a shifted impulse (at a time t=T₀ ) yields a shifted version of that function (also shifted by T₀). We prove this by using the definition of convolution (first line, below).

Why convolution is applicable on LTI systems only?

Convolution is an incredibly useful operation because it can be used to predict the output of an LTI system to any input.