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Fourier Series

This applet displays the individual Fourier components of the periodic rectangular function ƒ(t) shown in figure 1, and also demonstrates the addition of the components to form the function.

Rectangular waveFigure 1

The display is based on the Fourier decomposition of ƒ(t) according to

Fourier series.

The components have frequencies that are zero or integer multiples of the fundamental repetition frequency 1/T; ie fn=n/T. Fourier analysis of ƒ(t) shows that the amplitude of the components are given by:

Component amplitude.

The elements of the display are
Upper graph
Middle graph
Lower graph
a. selected sinusoidal component, or
b. an animation of the addition of the components

The interactive capability permits choice of the following:
The duty cycle τ/T Move slider in top left.
The number of components Enter in box (max. 100) and hit 'enter'.
Selected components Click on component in middle graph and use arrow keys to step through components.
Addition of components Slider and buttons on top right.
The sinc function envelope of the bn is best displayed with a low duty cycle and a high number of components.
Physics virtual library