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. |