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MathGroup Archive 2004

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Re: Finding the Fourier transform of discrete functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52661] Re: Finding the Fourier transform of discrete functions
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 7 Dec 2004 04:09:55 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <cohi1d$1fh$1@smc.vnet.net> <200412011057.FAA19902@smc.vnet.net> <comgk7$7a2$1@smc.vnet.net> <copa52$pmk$1@smc.vnet.net> <cos0k6$dgj$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

f[x_Integer]]/;1<=x<=12 = Sin@x

say that for a integer x in [1,12] the function can be simplifyed to
Sin[x], it say *not* that for other arguments the function
is indeterminate. The additional definition

f[_]:=Indeterminate

would do that.

Regards
  Jens

"Peter Pein" <petsie at arcor.de> schrieb im Newsbeitrag 
news:cos0k6$dgj$1 at smc.vnet.net...
> Jens-Peer Kuska wrote:
>> Hi,
>>
>> and you think that 1<=x<12 is discret, and not a infinite number
>> of continuous values ?? Strange !
>>
>> Regards
>>   Jens
>>
>> "DrBob" <drbob at bigfoot.com> schrieb im Newsbeitrag
>> news:comgk7$7a2$1 at smc.vnet.net...
>>
>>>>>what is a "discrete function".
>>>>>if it is a function, the parameter is continuous and FourierTransform[]
>>>>>compute the transformation.
>>>
>>>A discrete function is a function with a discrete domain.
>>>
>>>For instance, this is a discrete function on the obvious domain:
>>>
>>>f[x_Integer]/;1<=x<=12 = Sin@x
>     *^^^^^^^^*
>>>It is NOT the Sin function, for the simple reason that the domain of a
>>>function (in math or mathematica) is part of its definition.
>>>
>>>Bobby
>>>....
>
> I think, it's his firm conviction that there are only 12 Integers x in
> the interval 1<=x<=12. ;-)
>
> -- 
> Peter Pein
> 10245 Berlin
> 



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