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## Re: [Help-gsl] Question about Discrete Hankel Transform

 From: Hongzheng Wang Subject: Re: [Help-gsl] Question about Discrete Hankel Transform Date: Mon, 20 Sep 2010 20:30:08 -0400

```Hi Hongcheng,

I am sorry I made a mistake in my previous post.  Yes, you are right.
The samples should be on the zeros of the specific Bessel function,
ie, it is not a uniform sampling.

Let's go back to your question.  It seems to me that regenerating
required non-uniform samples from existing uniform samples would be
difficult or impossible unless you have the analytical expression of
the transformed function.

Best wishes,
HZ

On Mon, Sep 20, 2010 at 5:33 PM, Hongcheng Ni <address@hidden> wrote:
> Hi Hongzheng,
>
> Thank you for your reply!
>
> However, look at the third formula in that section (32.1) of the manual,
> gsl_dht does require the values of function f at zeros of Bessel
> function J_nu.
>
> -
> Best regards,
> Hongcheng Ni
> JILA, University of Colorado at Boulder
> 440 UCB, Boulder, Colorado 80309-0440
>
>
> On Mon, 2010-09-20 at 17:04 -0400, Hongzheng Wang wrote:
>> Hi Hongcheng,
>>
>> I am afraid you misunderstood the manual of GSL at this point.  Just
>> take a look at the following quoted sentence in the manual and make
>> sure you know what it means:
>>
>> ``compare this to the case of the discrete Fourier transform, where
>> samples are taken at points related to the zeroes of the sine or
>> cosine function.''
>>
>> In fact, to do a discrete Hankel transform of a particular function f,
>> you just need to provide a sequence of samples of f, which normally
>> are obtained indeed on a uniform manner.
>>
>> HZ
>>
>> On Mon, Sep 20, 2010 at 3:57 PM, Hongcheng Ni <address@hidden> wrote:
>> > Hi everyone,
>> >
>> > I'm a newcomer and have a question about discrete Hankel transform (DHT)
>> > in GSL package.
>> >
>> > By reading the manual, I find that gsl_dht only supports a non-uniform
>> > grid system in which sampling is done on the zeros of the Bessel
>> > function (of the first kind) J_0.
>> >
>> > Does anyone know how to use it on a uniform grid? (Because changing my
>> > existing code from uniform sampling to non-uniform sampling would cost a
>> > lot of time.) Thanks!
>> >
>> > -
>> > Best regards,
>> > Hongcheng Ni
>> > JILA, University of Colorado at Boulder
>> > 440 UCB, Boulder, Colorado 80309-0440
>> >
>> >
>> >
>> > _______________________________________________
>> > Help-gsl mailing list
>> > address@hidden
>> > http://lists.gnu.org/mailman/listinfo/help-gsl
>> >
>
>

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