Integrating Fourier Series Applet.

Cuthbert Nyack
An integrator has a transfer function which is inversely proportional to frequency and a constant phase lag of 90º.
Equation above shows the Fourier Series of a square wave with some terms in red added to show the effect of integration. As "a" changes from 0 to 1, the wave changes from a square wave (shown in magenta) to a triangle wave (shown in red). Applet below graphically illustrates the effect.

A corresponding equation and applet for the triangular wave is shown below.
Note that one of the effects of integration is to "smooth" the signal from a linear function of t to a quadratic function. Discontinuities in amplitude are transformed to discontinuities in gradient etc, and the Fourier series converges much faster.

When activated the following gif image show how the applets should appear.

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COPYRIGHT © 1996 Cuthbert Nyack.