Investigation of Optimal Linear Shift-Invariant Two-Dimensional Digital Filters.

This investigation develops an interactive computer-aided method for designing lowpass or highpass two-dimensional finite impulse response digital filters. Filters designed using this method will have linear phase and an equiripple error in the transmission and attenuation bands. The essence of the method is that it transforms an optimal one-dimensional digital filter into a close approximation of an optimal two-dimensional digital filter. The amplitude characteristic of the one-dimensional filter is preserved in the sense that each point of the one-dimensional frequency response is mapped to a contour in the two-dimensional plane. This transformation was first proposed by James H. McClellan, and is now called McClellan Transformation. By controlling the mapping of a specified one-dimensional frequency to a desired contour shape in the plane, two-dimensional filters of fairly arbitrary specifications can be designed that is, their frequency can be determined, and the associated two-dimensional impulse response coefficients calculated. Author