The operations of second derivative, analytic continuation, smoothing, the removing of residuals or regionals, and others in gravity and magnetic interpretation are analogous mathematically to the filtering action of electric circuits. The main difference between the two is that electrical filters act on functions of one variable (time), whereas the geophysical filters must act on functions of the two space variables (x and y). This paper develops linear filter theory for gravity and magnetic interpretation. As an application of the theory, downward continuation is discussed in some detail. The frequency response of upward continuation is an exponential function decreasing with increasing frequency. The inverse process of downward continuation has a frequency response which is the reciprocal of the upward continuation response. This paper discusses a method of matching frequency responses by coefficient sets and shows by examples some of the inherent difficulties in downward continuation. A final example calculated analytically shows how good a downward continuation can be expected from a finite coefficient set.