Fourier Series Study Guide
Periodic signals are signals that repeat with some period. Fourier Series can be used to represent periodic signals mathematically using a sum of sinusoidal signals at multiples of the basic (fundamental) frequency of repetition.
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Periodic signals are signals that repeat with some period. Fourier Series can be used to represent periodic signals mathematically using a sum of sinusoidal signals at multiples of the basic (fundamental) frequency of repetition.
- Why learn about Fourier Series?
- Periodic signals and signals that are almost periodic can be thought of as being composed of sinusoidal signals (i.e. sines and cosines) at different frequencies. Linear systems (electrical, mechanical, whatever) can be thought of as frequency sensitive or frequency selective systems that can operate to minimize or maximize the effect of those portions of a period signal at a particular frequency. In those systems, when you have an input/driving signal that is the sum of several signals, you can compute the effects of individual signals and then add the effects/responses of the individual signals to get the total response. Since a Fourier Series breaks periodic signals into a sum of many sinusoidal signals you can use that property to your advantage.
- Fourier Series are the key to understanding the FFT and other methods of frequency analysis, and you may use frequency analysis in bridge vibrations, aircraft noise analysis, seismic signals, and many other non-electrical phenomena. The Fourier Series was invented in the study of heat flow, so there is nothing about it that makes it a topic purely for Electrical Engineers.