Fourier 1

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.

Figure 1

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

.

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

.

The elements of the display are

Upper graph: ƒ(t)
Middle graph: b_n
Lower graph: a. selected sinusoidal component, or
b. an animation of the addition of the components

The interactive capability permits choice of the following:
	Action
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.

Notes

The sinc function envelope of the b_n is best displayed with a low duty cycle and a high number of components.