Convolution of shifted signal [closed]

1. What is convolution of 2 signals?
2. What is the convolution of a signal with an impulse?
3. Why do we convolve two signals?

What is convolution of 2 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. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response.

What is the convolution of a 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 do we convolve two signals?

Convolution is a mathematical tool to combining two signals to form a third signal. Therefore, in signals and systems, the convolution is very important because it relates the input signal and the impulse response of the system to produce the output signal from the system.