MHB Why Use Half Range Fourier Series for Functions Like x and x^2?

[matqkks]

If we have a standard function like x or x^2 defined between 0 and pi. Then why should we be interested in extending this function to give a Fourier series which resembles this function between 0 and pi? What is the whole purpose of this process? Does it have any real life application or is it just a mathematical exercise?

 

[I like Serena]

If we have a standard function like x or x^2 defined between 0 and pi. Then why should we be interested in extending this function to give a Fourier series which resembles this function between 0 and pi? What is the whole purpose of this process? Does it have any real life application or is it just a mathematical exercise?

Hi matqkks!

If we have $x$ between $0$ and $\pi$ and extend it to give a Fourier series, we have a sawtooth or triangle signal.

This type of signal is used for instance in a (CRT) television for tracing the pixels on the screen.