Re: IS this for real?!

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 08/18/04 

Date: Wed, 18 Aug 2004 00:27:58 +0200

Matt Mahoney wrote:

> "Mok-Kong Shen" <mok-kong.shen@t-online.de> wrote:

>>Douglas A. Gwyn wrote:
>>
>>[snip]
>>
>>>the Heisenberg uncertainty principle, which is a
>>>direct consequence of a standard fact about Fourier
>>>transforms.
>>
>>Could you kindly elaborate this a little bit in a way
>>that a layman can understand? Thanks.

>
> Suppose you have a sine wave (e.g. sound) that varies in freqency over time,
> and you ask what the frequency, f, is at some instant in time, t. If you
> take a broad time window around t, you can measure the frequency fairly
> accurately by counting the number of cycles, but there is an uncertainty
> about t (call this dt). If you decrease dt, then you increase the
> uncertainty, df, in the frequency. The uncertainty principle says that the
> best you can do is df*dt >= 1.

My problem is that I am not aware of a book on Fourier transform
that (explicitly) mentions the inequlity above. If you happen
to know one, please kindly tell me.

M. K. Shen