We present two automatic algorithms, which use the Wiener-Hopf least-square method, for the calculation of digital linear filters for sine, co-sine transforms and J0, J1 and J2 Hankel transforms. The first algorithm optimizes the following parameters: abscissa increments, initial abscissas and displacement factor for the computation of digital linear filters coefficients that are computed through sine and co-sine analytic transforms. The second algorithm optimizes the following parameters: abscissa increments and initial abscissas for the computation of digital linear filters coefficients that are computed through J0, J1 and J2 Hankel analytic transforms. This methodology led to the proposition of new digital linear filters of 19, 30 and 40 points for the co-sine and sine transforms, and to new optimized filters of 37, 27 and 19 points for the J0, J1 and J2 Hankel transforms, respectively. The comparison of the performance of these filters with respect to the others ones published in the geophysical literature is evaluated by using a analytical geophysical model composed of two half spaces. An infinite current line was used between the half spaces, giving rise to the sine and co-sine transforms. Among all simulations carried out, it was noticed that the new sine and co-sine transforms of 19 points presented better performance when compared to the existing ones in the literature. In addition, J0 and J1 transforms were obtained using a vertical magnetic dipole as source between the half spaces, noticing that better performances using the new J1 filter of 27 points were obtained among all simulations when compared to the existing 47 points J1 filters, as well as with the simulations carried out using the new 37 points J0 filter and compared with the 61 points J0 existing filters in the literature. Using a horizontal magnetic dipole between the half spaces, it was observed an equivalent performance using the 37 and 27 points new filters for the J0 and J1 transforms when compared, respectively, to the existing 61 and 47 points filters in the literature. Finally, it was observed an equivalent performance using 37 and 27 points new filters for the J0 and J1 transforms when compared, respectively, to the existing 61 and 47 points in the literature, and when applied, respectively, in Wenner and Schlumberger electrical soundings. Most of our filters contain fewer coefficients than those usually used in geophysics. This aspect is very important because these linear filter transforms are commonly used intensively in numerical massively geophysical problems.
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