I found a filter for Hankel Transform . As far as i understand this is effectively used as an approximation for $J_0(x)$ and $J_1(x)$.

But how will the change in input affect these filter terms (e.g. $J_0(r) \rightarrow J_0(2r)$)

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References : http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2478.1997.500292.x/full

  • $\begingroup$ Your question "But how will the change in input affect these filter terms ...?" is unclear. What are "these filter terms"? Please clarify what you don't understand. $\endgroup$ – Matt L. Jun 3 '15 at 7:46
  • $\begingroup$ for example : If I change the input from J0(x) to J0(2x) how does this affect then filter terms shown in table one(figure) ? $\endgroup$ – shrey Jun 3 '15 at 8:10

I think you misunderstand what this filter is doing. It does not compute approximations of the Bessel functions $J_0(x)$ and $J_1(x)$, but it computes an approximation of the Hankel transform of some input function. The function is expressed as a weighted sum of Bessel functions, and the result of the transform are the weights. The digital filtering approach is an efficient alternative to solving the transform integral by standard methods of numerical integration.

  • $\begingroup$ this fact has been illustrated in this figure : i.stack.imgur.com/EMg30.jpg . Regarding my doubt consider equation 9 : if F is a vector then Z is also a vector.but in next equation we have F as a vector and H as row vector and after summation this makes Z a scalar. where am i making a mistake here ? $\endgroup$ – shrey Jun 4 '15 at 2:17

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