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.

return to demonstrations page

Applet by Hsi Chen Lee.