Convolution and Its Physical Meaning

Introduction

I find many explanations of convolution on its physical meaning on the internet. I am surprised that most of them are wrong. Therefore, this attempt is to make a logical and correct explanation of the physical meaning of convolution. 

An animation of a convolution of two signals. Considering a physical system, we consider f(x) to be the input and g(x) to be the impulse response of the system. (f*g)(t) is the system output which is the convolution between f(x) and g(x).

Impulse function

Approaching a Dirac-delta function using a zero-centered Gaussian distribution function and a rectangular function.

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