Electric Circuits and Networks

13.6 PROPERTIES OF FOURIER SERIES AND SOME EXAMPLES

Let us take some examples of Fourier series and develop the important properties of this series through them. The waveforms used in the examples that follow are very important signal waveforms that appear frequently in Electrical and Electronic Engineering applications and are not just some functions used to illustrate Fourier series. The waveforms appearing in the examples are important in their own right.

The first property of Fourier series is almost self-evident. It is the property of linearity. It states that if v₁(t) and v₂(t) are two periodic waveforms with the same period T and v₃(t) = a₁v₁(t) + a₂v₂(t), then,

for all n, where _1n, _2n and _3n are the coefficients of exponential Fourier ...