Hankel transform filters for dipole antenna radiation in a conductive medium

We discuss the Hankel transforms related to a particular application, i.e. the dipole antenna radiation in conductive media, such as the antenna radiation in sea-bed electromagnetic applications. In this application, the electromagnetic wavefields decay very rapidly with distance. A good filter means that it can be used to evaluate weak fields. Exponential sampling transforms a Hankel transform into a convolution equation, which must be solved to obtain the filter coefficients. Here, we use a direct matrix inversion method to solve the convolution equation in the sample domain, instead of the Fourier transform method and the Wiener–Hopf method, previously used to solve the convolution equation. This direct method is conceptually simple and is suitable for our optimization process: by using the Sommerfeld identity, we search for the optimum sampling interval, which corresponds to the minimum wavefield, evaluated for a given length filter. The performances of the new filters obtained are compared with some well-known filters. We find that our filters perform better for our application; that is, for the same length filters, our filters are able to calculate weaker fields. For users working in similar applications, three sets of filters with lengths 61, 121, 241 are available from the author.