Qingling, I don't understand the role of the Hankel transform in your question. Why not simply compute the convolution using DFTs?
Brian On Thu, Mar 15, 2012 at 9:00 AM, <help-gsl-requ...@gnu.org> wrote: > > Date: Thu, 15 Mar 2012 17:12:18 +0800 > From: ??? <sunac...@gmail.com> > To: help-gsl@gnu.org > Subject: [Help-gsl] A question about the Discrete Hankel Transform > > Hi all, > Sorry for disturbing, this is the first time I am using mailing lists and > don't know whether this is a proper place to ask questions. But I > encountered some problem and really need some help. > I am encontered some problem in calculating the inverse hankel transform of > functions. Let's say the function is R=[r1,r2,r3,r4], I used gsl_dht_apply, > in > > http://www.gnu.org/software/gsl/manual/html_node/Discrete-Hankel-Transform-Functions.htmlto > get the hankel transform, like this gsl_dht_apply(dht,R,R_out) and > used > gsl_dht_apply(dht,R_out,R_prime) to get the inverse transform. It satisfies > R=coef*R_prime, where coef=j_(\nu,M) according to the documentation of > gsl_dht_apply function. > And now my problem is that for two functions R=[r1,r2,r3,r4] and > T=[t1,t2,t3,t4] in time domain, I want to compute the convolution of them > according to the Convolution Theorem, saying that the convolution of two > functions in time domain is the inverse Fourier Transform of two functions > element-wise multiplication in the frequency domain, and Hankel Transform > of the 0-order Bessel function of first kind is equal to 2D fourier > transform. Let's say R_out=[ir1,ir2,ir3,ir4] and T_out=[it1,it3,it3,it4] > are the inverse hankel transform of R and T respectively. Let F be the > element-wise multiplication of R_out and T_out, that is > F=[ir1*it1,ir2*it2,ir3*it3,ir4*it4]. Then how can I get the original > convolution result of R and T? Is it still R**T=coef*F_out or should I > multiply some other coeficient?(** stands for convolution and F_out is the > inverse hankel transform of F, coef=j_(\nu,M)). > Thanks for help! > > -- > ??? > Qingling Zhang > Institute of CG & CAD > School of software Tsinghua University > Tsinghua University Beijing, P.R.China 100084 >