The trace left by the French mathematician and physicist Jean-Baptiste Joseph Fourier in the history of science is very deep. Being born into a humble family in the late 18th century didn’t stop him from reading and unleashing a well-channeled innate creativity. two great mathematicians like Pierre-Simon Laplace and Joseph-Louis Lagrange, who taught him at the Ecole Normale Superior in Paris.

His contributions in both physics and mathematics are invaluable, but one of them has contributed decisively to the development of telecommunications and digital processing of information. In fact, without this knowledge, it would be very difficult for them to be this successful until they reach their current development. However, with the unexpected turn of events, Fourier’s most meaningful contribution in this field continues to frighten many students with scientific careers.

The Fourier transform helps us understand nature a little better.

Math often requires us to perform great effort at abstraction. In fact, this is exactly where the challenge for many people lies. What is out of the question is their enormous relevance and profound impact on many of the sciences with which they coexist and complement. The math involved in the Fourier transform is advanced, so understanding it as a whole and dealing with it fluently is not easy. Even so, it’s worth flirting with him at least to know what he is and what his applications are.

In this article, we do not need to explore the mathematical basis of the Fourier transform, but we are interested in knowing that it is a mathematical operation that allows us to move a function into the frequency domain. It’s a bit of a complicated definition, true, but we can also see it as a mathematical transformation that helps us extract the frequencies that make up a function. In practice, this resource is very useful for tackling many functions that lie in the mathematical basis of computing and telecommunications.

The mathematical expression of the Fourier transform is daunting. At least a little.

The video below explains it in a clear and reasonably accessible way what is the fourier transform. Its author, content creator 3Blue1Brown’s greatest contribution is that he has always been meticulous and has managed to describe it visually in order to alleviate the effort of abstraction that we must do. This video takes almost 21 minutes but it’s so worth it. Engaged.

What we’ve seen so far helps us intuit precisely what this mathematical operation consists of, but we haven’t yet explored the most important thing: what it does and the role it plays in many of the technologies we use every day. Its applications are so numerous and so relevant that we will need a multi-page book to collect them all, but at least we can flirt with some of them.

In the field of telecommunications, the Fourier transform helped us find the way. transmit signals via electromagnetic waves separates them into component frequencies. This technology is essential when it comes to exploiting the entire radio spectrum, and without it the radio, television, mobile phone and wireless networks as we know it would not be possible. As you can see, this mathematical operation is somehow a part of our life.

However, this is by no means all. The engineers of the RCA company, which invented color television in the 1950s, used the Fourier transform to greatly simplify color coding and significantly reduce the signals that had to be transmitted.

It even has a leading role in the strategy used by our computers. processing information efficiently. It’s impossible to know how technology would evolve without this tool handed to us by Fourier and other mathematicians, but we can be sure of one thing: our world would not be what it is today.

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