This report documents the techniques used to filter quantities on a stretched grid general circulation model. Standard high-latitude filtering techniques (e.g., using an FFT (Fast Fourier Transformations) to decompose and filter unstable harmonics at selected latitudes) applied on a stretched grid are shown to produce significant distortions of the prognostic state when used to control instabilities near the pole. A new filtering technique is developed which accurately accounts for the non-uniform grid by computing the eigenvectors and eigenfrequencies associated with the stretching. A filter function, constructed to selectively damp those modes whose associated eigenfrequencies exceed some critical value, is used to construct a set of grid-spaced weights which are shown to effectively filter without distortion. Both offline and GCM (General Circulation Model) experiments are shown using the new filtering technique. Finally, a brief examination is also made on the impact of applying the Shapiro filter on the stretched grid.Takacs, Lawrence L. and Sawyer, William and Suarez, Max J. (Editor) and Fox-Rabinowitz, Michael S.Goddard Space Flight CenterATMOSPHERIC GENERAL CIRCULATION MODELS; ASSIMILATION; MATHEMATICAL MODELS; SPATIAL FILTERING; DATA INTEGRATION; COMPUTATIONAL GRIDS; STABILITY; GEOS SATELLITES (ESA); EIGENVECTORS; NONUNIFORMITY; FAST FOURIER TRANSFORMATIONS; POLAR REGIONS; FREQUENCY RESPONSE; HARMONICS; STRETCHING; FINITE DIFFERENCE THEORY...