Re: finite duration to infinite bandwidth
- From: Bob Monsen <rcsurname@xxxxxxxxxxx>
- Date: Wed, 04 Jan 2006 19:49:17 -0800
On Tue, 03 Jan 2006 17:06:46 -0800, rdysydc wrote:
> Hi,
>
> I know a signal of finite time duration has infinite bandwidth, and vice
> versa. But how to prove it? I tried to get something starting from
> Fourier transform pair but failed.
>
> Thanks!
>
> chi
Given interval T, if I assert that this interval T can only have signals
of finite bandwidth, then there must be a largest frequency F(T) that
exists on the interval. But it is clear that the signal sin(2*PI*2*F(T)*t)
has a higher frequency on this or any interval. Thus, it is not possible
to choose a highest frequency, so the bandwidth is infinite. Is this what
you are looking for?
I don't know what you meant by 'vice versa'.
--
Regards,
Bob Monsen
"I have no great quickness of apprehension or wit which is so
remarkable in some clever men, for instance Huxley"
-- Charles Darwin
.
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- From: rdysydc
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