Computer programs for designing two-dimensional recursive digital filters via digital spectral transformations

FORTRAN computer programs are developed for designing two-dimensional (2-D) circularly symmetric recursive digital filters from a one-dimensional (1-D) lowpass prototype using digital spectral transformations (DST's). The DST technique was employed to take advantage of the readily available 1-D filter design software. Also, the DST design method requires no numerical iteration and is relatively simple to program.

A survey of available DST design techniques is given. A choice is then made from among the various techniques. A detailed discussion of the selected technique is given. This technique and its computer program implementation provide a 2-D lowpass digital filter from the 1-D lowpass prototype. A second computer program then applies two l-D DST's to transform the 2-D lowpass filter to other 2-D filter types (lowpass with a different cut-off contour, highpass. bandpass, and bandstop). Several filter designs are carried out to verify that the filters obtained using this technique have magnitude contours of a proper shape to be of practical use.

The problem of realizing the filters designed is also briefly considered. The design programs are written to output the 2-D filter coefficients in the form needed for realizing the filter using a canonical real-gain Roesser's local state-space structure. This structure was selected because it is suitable for subsequent optimization with respect to finite wordlength effects.