Fourier Series: Continuous, Periodic Time Series

 

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: