A
real, *T*-periodic signal *x(t)*
can be represented by a *Fourier
series*

_{}

where
_{} is the *fundamental frequency* and each _{} is nonnegative (by
adding *p* to _{} if necessary).

This
expression also can be written as the real part of a phasor sum

_{}

For
a gentle introduction to this topic, visit the lecture Harmonic Phasors and Fourier
Series.

Since
projection on the real (horizontal) axis is inconvenient for portrayal, we
rotate each phasor by *p**/2* radians and project on the vertical axis.
This makes use of the mathematical relationship

_{}

In
the applet there are four options for displaying a Fourier series with up to 25
terms:

·
select
from the provided signals,

·
sketch
one period of a signal,

·
construct
a phasor sum by successively clicking on the complex plane,

·
enter
data (the _{}, magnitude and angle) in a data table.

Amplitude
units are marked on the complex plane, and the angles are in degrees.

Applet by Hsi Chen Lee. |