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Applications of mathematics in Real Life, Fourier Transform.
Fourier Transform is a mathematical tool that is used to study the complex waves. It takes a periodic function, whatever that is, and decomposed it into its elementary waves which are more simple and easier to treat. Without a physical sense, the notion of fourier transform is an abstract concept, but it is when we consider their applications when you see their true value.

In nature waves are everywhere, they are the main form of propagation of the energy in the universe and without them the world we know would not exist. According to its size, its forms and its frequency range, number of complete cycles per second, they will have a greater or less amount of energy and different characteristics.

As examples of waves we have the sound and the light. In the case of sound, the number of oscillations per second gives us the height of the sound, as more oscilations has, more acute is the sound and the wave amplitude gives us its volume. A complex wave would be one thar result from the sum of all the sounds of the instruments in an orchestra, for example.

The same applies to the light, the oscillation rate gives us the color, an oscillation very high makes light looks blue and a very low makes it looks red, the amplitude makes it looks more or less bright. With the light a complex wave, sum of some colors, makes light looks white.

After seeing how complex the waves can be, it is essential and necessary to break them down for thus can be studied and characterized easily, and that is when comes Fourier Transform.

Fourier transform what it does is take the sound of an orchestra and separates each of their instruments, take a light beam and separates it into its primary colors, it takes a wave and says which are its elementary waves. This is a great application of Fourier Transform and thanks to it, the technology can advance and science improve.