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.

How Language Shapes the Way We Think

Do you know that there are some people who are obsessed with learning new languages? Have you ever felt that how can someone waste their time in such an unproductive thing? I also once could not understand those people who love languages. What is there to love about a language? How come one language be more beautiful, while another be more elegant, and the other be more logical? Now I think I can understand these perceptions.

I came to Japan at the age of 19. I learned Japanese for one year, then completed my bachelor in Japanese. I am a university teacher now engaging with Japanese people in the Japanese language every day. Many foreign students and researchers come to Japan temporarily for study and research. Among them, some become hateful of the Japanese language. There may be many reasons for becoming hateful such as difficulty, usage of Kanji, etc. There is another reason not directly associated with language structure or grammar. The reason is that what benefit can the Japanese language give me after I leave Japan. It will be a waste of time trying to learn the Japanese language. Unsurprisingly, people with this mentality can never learn a new language. They see language as a tool for their business. Yes, languages are tools for communication. But, they miss an important perception that one’s thought process is shaped by the languages he/she knows. Knowing many languages will raise your thinking ability, give you the ability to view and analyze things in different ways, you will have the luxury of understanding in multiple ways and synthesize a new understanding on the matter.  I tried to explain this concept to some of them only ending in unfruitful results. I did not have the theory and data to support my claim.

I am happy that finally, I have found some research works on this topic. Please watch the following videos.