Re: Re: Re: FourierTransform of Sinc Function

• To: mathgroup at smc.vnet.net
• Subject: [mg44418] Re: [mg44359] Re: [mg44311] Re: FourierTransform of Sinc Function
• From: Yasvir Tesiram <yat at omrf.ouhsc.edu>
• Date: Sat, 8 Nov 2003 04:50:59 -0500 (EST)
• References: <200310281053.FAA25777@smc.vnet.net> <bo7of6\$ag8\$1@smc.vnet.net> <200311051500.KAA26329@smc.vnet.net> <200311071016.FAA05356@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Fourier is a bit of a pain if you are going to work with real data as
in a pulse or discretely sampled signal where the FourierParameters a
and b are obviously related to the sampling rate of your data.  This is
not so clear from the documentation, which says that the output is not
Mathematically relevant if you use different values for the
FourierParameter other than an integer that is not related to the
length of the input.  I don't know exactly what it means. It seems to
be a bit of a catch 22 kind of message. The following is by trial and
error and you should really go back and try and relate the
FourierParameter to the sampling of your signal or pulse and put that
in the context of the spectrum. The plot is the power spectrum of the
sinc pulse.

pulse = Table[Sin[x]/x, {x, -5 N[Pi], 5 N[Pi], N[10. Pi/301.]}];
ListPlot[pulse, PlotRange -> All];

ftpulse = Re[Fourier[pulse, FourierParameters -> {0, N[10. Pi/602]}]];
ftpulse2 = Im[Fourier[pulse, FourierParameters -> {0, N[10. Pi/602]}]];
halfpower = Sqrt[(ftpulse)^2 + (ftpulse2)^2];
reversehalfpower = Reverse[halfpower];
fullspec = {reversehalfpower, halfpower} // Flatten;

ListPlot[fullspec, PlotRange -> All, PlotJoined -> True]

Yas

On Nov 7, 2003, at 4:16 AM, Kieng wrote:

> I am sorry my question is apparently not so clear.
> I generated a list of data from a sinc function.  I am not doing the
> transform from the sinc function.
> If I use Fourier[list of the data], and plot the result, her is where
> I am
> kind of not sure why I don't get a top hat function, even though I
> used very
> fine step for my sinc function data.
>
> ----- Original Message -----
> From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg44418] [mg44359] [mg44311] Re: FourierTransform of Sinc Function
>
>
>> Hi,
>>
>> what is mysterious on
>>
>> In[]:=FourierTransform[Sin[w*x]/x, x, k]
>>
>> Out[]=(Sqrt[Pi/2]*(-Sign[k - w] + Sign[k + w]))/2
>>
>> Regards
>>   Jens
>>
>> Kieng wrote:
>>>
>>> Dear All,
>>>
>>>  I tested the Fourier Function on a sinc function which should give
>>> the
>>> top-hat but mathatmatica gave some mysterious plot that I don't
> understand.
>>> Anyone knows what is going on.
>>>
>>> Thank you very much,
>>> Sorasak
>>

```

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