Re: Gaussian Shaped signal has a fourier transform

From: Gordon Sande (g.sande_at_worldnet.att.net)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 15:09:58 GMT

G Kannan wrote:
> Sir,
> Is there any other functions which has the same shape in time
> and frequency domains like gaussian?
>

The extended function, also called a distribution by many
mathematicians, consisting of an infinite sequence of equally
spaced delta functions also shares this property. This extended
function is usually called a delta comb.

It provides a quick way to represent either sampling or periodic
replication when one either multiplies of convolves with it. As
a exercise you might consider doing both to get periodically replicated
sampled sequences. Beware the trap for the unwary of having a unit
spaced sample in a replication period of one.