The gaussian is an example of a self reciprocal function, ie both function and its transform has the same form. The time and frequency functions are shown below.

In the applet below, f(t) is in red, F(w) is in green. The product is shown in yellow. both time and frequency ranges are ±2.5. The product has maximum width when a = 0.5.

COPYRIGHT © 2005 Cuthbert Nyack.