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.