If a signal is continuous and periodic in time, it can be represented by a sum of sine and cosine waves known as the Fourier Series. The Fourier series is discrete in frequency, i.e the sinusoidal components occur at discrete frequency values.
For a more compact Fourier series notation, Euler's formula is used to combine the sine and cosine terms into one expression.
A continuous periodic time series with period T has the following Fourier series expansion:
