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.

 

 

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Applet by Hsi Chen Lee.