Published May 19, 2022 - By Marco Garosi
Fourier Series is a mathematical tool, named after French mathematician Joseph Fourier, that allows us to decompose a periodic function as a sum of sine and cosines waves. Each of those sines/cosines has a frequency which is an integer multiple of the periodic function’s fundamental frequency. Fourier Series is a fundamental part of signal processing and will later be extended with the Fourier Transform, which extends it to non-periodic signals.
A Fourier Series is a sum of sine waves and is so defined (synthesis equation):
Every “iteration” has to be provided a value. values can be computed with the so-called analytis equation:
If (so if ), then in the synthesis equation gets scaled only — it has no initial phase.