  "Cluster" extensions of the dynamical mean field method to include longer
range correlations are discussed. It is argued that the clusters arising in
these methods are naturally interpreted not as actual subunits of a physical
lattice but as algorithms for computing coefficients in an orthogonal function
expansion of the momentum dependence of the electronic self-energy. The
difficulties with causality which have been found to plague cluster dynamical
mean field methods are shown to be related to the "ringing" phenomenon familiar
from Fourier analysis. The analogy is used to motivate proposals for simple
filtering methods to circumvent them. The formalism is tested by comparison to
low order perturbative calculations and self consistent solutions.
