Summary: Signals can be composed by a superposition of an infinite number of sine and cosine functions. The coefficients of the superposition depend on the signal being represented and are equivalent to knowing the function itself.

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In Signal Decomposition , we have shown that we could express the square wave as a superposition of pulses. This superposition does not generalize well to other periodic signals: How can a superposition of pulses equal a smooth signal like a sinusoid? Because of the importance of sinusoids to linear systems, you might wonder whether they could be added together to represent a large number of periodic signals. You would be right and in good company as well. Euler and Gauss in particular worried about this problem, and Fourier got the credit even though tough mathematical issues were not settled until later. They worked on what is now known as the Fourier series.

Let
*harmonically *related sine waves.