Optimization of short digital linear filters for increased accuracy

Abstract

The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest. As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter. The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.