Twentieth class, Fourier, obviously, Rules

We have triggered the class with a question: what happens when we have periodic non-sinusoidal signals? That's when we can apply the Series of Fourier. Fourier was a mathematician who stated that every function can be expressed as a sum of sinusoidal functions in order to ease the calculus. 

In a circuit we can convert a periodic non-sinusoidal signal generator into a series of sinusoidal generators which obey to the statement: the more they are, the more precise the supposition will be. Bearing this at mind, we have introduced the concept of spectrum, a representation of the amplitude of each term of the series, which depends on the root mean square value of the signal and become lower with every step in the series. We also have a Fourier spectrum for the phase of each term of the series, but this time the values get equal during all the series, as the phase of a circuit usually changes once or twice as maximum, as seen in Bode diagrams. 

We can't learn without the help of examples, so it has been incredibly useful to see the spectrum that relates to a squared signal. Also, we have checked the effectivity of that method considering just three terms of the series and proving that it has been a very good approximation. We will continue talking about this topic in the next class.