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Fourier Series - Coggle Diagram
Fourier Series
Applications
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Shazam (music recognition) 
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Properties
Parseval's theorem
The average value of the square of a function is equal to the sum of the average values of the square of the Fourier components
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Plancherel's theorem
It states that the integral of a function's squared modulus is equal to the integral of the squared modulus of its frequency spectrum
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A fourier series decomposes periodic functions or periodic signals into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines( or complex exponentials).
It's useful in Physics because it allows to detect and analyse periodicities in apparently random functions
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