Definitions of 'Bandwidth' and 'Time Duration' of Signals Which Are Connected by an Identity

In this paper we give definitions of "equivalent time duration"
\Delta\tau
and "equivalent bandwidth"
\Delta f
and show that they are connected by a simple reciprocal identity. An example is given and it is shown that the same concepts can be applied in antenna theory to give useful definitions of "equivalent aperture distribution width" and "equivalent angular spectrum."