| Elemental-filter design considerations - :12736 | National Weather Service (NWS)
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Elemental-filter design considerations
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    "In Office Note 165, Shuman noted that the G-filter (a seven-point operator) used in the LFM postprocessor can be simulated by using three 3-point symmetric smoothing elements of the type he developed in his 1957 Monthly Weather Review paper on smoothing and filtering in NWP. In this note, I will show how the relation given by Shuman for the G-filter relates to the design criteria for that filter, developed in Office Note 57. I then show how the progression from the five-point operator, called the H-filter by Shuman, to the G-filter can be both extended and modified. On the way, we encounter complex roots for a filter response function which leads to an application of Shuman's method for avoiding complex weights through the use of antisymmetric three-point elemental operators. Finally, I'll sketch a procedure for the calculation of the appropriate three-point symmetric or antisymmetric elements that satisfy a large set of conditions on the filter response function"--Introduction.

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