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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.

In Praise of Slowness

Life is about moving slowly and enjoying every bit of it. However, in today’s world, everybody seems to be rushing for everything. We are always fighting with time, trying to do many things at a time. Yes, it’s true that time is running very fast. But, shall we let ourselves to be consumed by time? No, we should put ourselves above time. We can accept that there are limitations on how fast we can digest and how fast we can perceive. Often, it is better to do things slowly. Doing things slowly doesn’t mean that you are wasting time. It means that you give more thought to your work, you let your creative mind to take control. you plan before, during and after. You give attention and focus to your work. You actually remember what you have done. You actually enjoy what you are doing. You always update yourself, educate yourself and continue doing it. So, let’s praise slowness. Let’s enjoy our life to its fullest.