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. |