A Review of Recursive and Implicit Filters

Low- and high-pass traditional recursive and implicit filters are reviewed. Some similarities and differences between these two forms are illustrated. The use of recursive filters in signal processing is contrasted with the needs in meteorology. The standard techniques used in building a recursive filter with specified characteristics are described. The desirability of high-order calculations is demonstrated. Some numerical results are presented to illustrate the differences in filter selectivity in the presence of topography. To make the implicit filters competitive with the traditional recursive formalism, efficient numerical matrix inversion procedures are employed in the application of both limited area and cyclic boundary conditions.