Spectral transformations for two-dimensional digital filters

A theory is developed for spectral transformations for two-dimensional digital filters. It is proved that these transformations take the form of stable two-dimensional all-pass functions and that the result of spectral transformation is stable if the original transfer function is stable. Emphasis is placed on formulating the transformations in a way which makes them easy to use for design, and it is shown that twodimensional spectral transformations offer a means of quickly obtaining new designs from previous ones. Included is a discussion of applications such as the design and realization of two-dimensional digital filters with tunable characteristics.