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!
-- 张庆岭 Qingling Zhang Institute of CG & CAD School of software Tsinghua University Tsinghua University Beijing, P.R.China 100084
