In essence ...

Jean-Baptiste Joseph Fourier

Joseph Fourier is one of my heroes as virtually everything one sees, hears or feels in system is due to this man's genius in creating the Fourier Transform, something, IMHO, as important as the two relativity theories of Einstein or the discovery of Quantum Mechanics in 1900.

The Fourier transform relates the time domain, in red, with a function
in the domain of the frequency, in blue. The component frequencies,
extended for the whole frequency spectrum,
are shown as peaks in the domain of the frequency.

Here is what it does to a C Major Chord

The Fourier transform applied to the waveform of a C major piano chord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G). The remaining smaller peaks are higher-frequency overtones of the fundamental pitches.

In English ... :)

The Fourier transform breaks a function down into wavelike building blocks.

Sierra Boucher; Samuel Velasco/Quanta Magazine

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies. When the combined sound wave descends through the ear canal and into the spiral-shaped cochlea, hairs of different lengths resonate to the different pitches, separating the messy signal into buckets of elemental sounds.

In the early 1800s, the French mathematician Jean-Baptiste Joseph Fourier discovered a way to take any function and decompose it into a set of fundamental waves, or frequencies. Add these constituent frequencies back together, and you’ll get your original function. The technique, today called the Fourier transform, allowed the mathematician — previously an ardent proponent of the French revolution — to spur a mathematical revolution as well.

Out of the Fourier transform grew an entire field of mathematics, called harmonic analysis, which studies the components of functions. Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics, from number theory to differential equations to quantum mechanics. You can also find the Fourier transform at work in your computer, allowing you to compress files, enhance audio signals and more.

A final word. 

It has been used to study the tides, to detect gravitational waves, and to develop radar and magnetic resonance imaging. It allows us to reduce noise in busy audio files, and to compress and store all sorts of data. In quantum mechanics — the physics of the very small — it even provides the mathematical foundation for the uncertainty principle, which says that it’s impossible to know the precise position and momentum of a particle at the same time. You can write down a function that describes a particle’s possible positions; the Fourier transform of that function will describe the particle’s possible momenta. When your function can tell you where a particle will be located with high probability — represented by a sharp peak in the graph of the function — the Fourier transform will be very spread out. It will be impossible to determine what the particle’s momentum should be. The opposite is also true.

In essence, the FT replicates reality when expressed by every digital system in the entire world. - Robert E.