Here is the link to the Wikipedia article on this topic.
keywords:
[a mathematical transform that decomposes functions]
[functions depending on frequency]
[a complex-valued function of frequency]
[Fourier series]
[complicated but periodic functions]
[complicated periodic functions]
[the properties of sine and cosine]
[trigonometric sine function]
[trigonometric cosine function]
[recover the amplitude of each wave]
[linearity]
[time-scaling]
[time scaling]
[conjugation]
[invertibility]
[periodicity]
