https://www.matongxue.com/madocs/473.html
https://www.zhihu.com/question/19714540 article written by really good.
1 intuitive explanation
may present a color light after 1666 Newton discovered the sunlight refracted through the prism, a phenomenon called dispersion of light:
Start with a physical sense, light is a wave, and the color of the light is determined by the amplitude and frequency.
In fact it is the dispersion of white light wave is decomposed into a seven-color light wave (actually a myriad of colors should be light waves):
Rainbow light waves can be a sine wave ansin (nx) (where an amplitude, nx represents frequency can) be approximated. So actually the Fourier series (just below the Fourier series of very inaccurate approximation, in order to help simplify the understanding becomes like this, so I am filled with guilt, the back will be given strict definition) above:
storm, sometimes you will see a rainbow:
Rain moisture in the air as if countless Mitsubishi mirrors, sunlight split into color. It dispersion phenomena of nature.
This is probably our most easily observed in nature Fourier series.
In nature there is a sequel to this story, we continue to go on.
German chemist Robert Bunsen (1811 a 1899), invented the Bunsen burner:
Bunsen burner in addition to high temperatures, there is a notable feature, and if the component controlling the fuel injection pressure of the sound, the flame may be no color.
Occasional cases, Bunsen sprinkled on the salt (sodium chloride) to light the flame:
originally colorless yellow flame becomes:
This is in fact the combustion of the sodium salt of colors.
Different chemical elements when burned have different colors, the color of the composite material combustion can be synthesized by the combustion of the color component of its decision.
So, if we want to detect components of a substance can be lit it, then its Fourier series decomposition of light, you can get components.
In this sense, everything Jieke Fourier series decomposition, which is its discoverer Baron Joseph Fourier (1768-1830) are convinced that the (in fact, there is a certain limit, this is more mathematics, You can view the convergence theorem of Fourier).
Well, intuitive explanation finished, it is no use eggs.
Like "I've heard a lot of sense, still too bad in this life."
We need more in-depth understanding in order to accompany Fourier had a good finish in this life.
2:00 domain: Fourier series rotation and
more detailed derivation, see this article: How to understand Fourier series formula? . https://www.matongxue.com/madocs/619.html
I can not wait to be given a strict form of Fourier series to make up for my previous approximation.
Suppose, f (x) is a function of period T and Fourier series convergence condition is satisfied, it can be written as a Fourier series:
among them:
2.1 Euler's formula
Euler's formula:
we can infer that:
According to the above equation, we can write another form of Fourier series:
where:
see the complex and do not be afraid, according to my previous article "How to be easy to understand ? explain Euler's formula "see something like 
this should think of rotation:
From this perspective, the Fourier series:
