ON THE DESIGN OF A BROAD CLASS OF 2-D RECURSIVE DIGITAL-FILTERS WITH FAN, DIAMOND AND ELLIPTICALLY-SYMMETRICAL RESPONSES

This paper deals with the design of a broad class of 2-D recursive dig ital filters including general fan, diamond and elliptically-symmetric filters. At first, the explicit design of quadrant and +/- 45-degrees fan filters is reviewed. A full-plane diamond filter (both axes are n early of length 2 pi) can easily be obtained through an appropriate tr ansformation of a +/- 45-degrees fan filter. Using this diamond filter as a prototype, a very simple spectral transformation is then propose d to design full-plane circularly-symmetric filters (radius almost-equ al-to pi). These filters share the same lattice wave digital structure and employ only first or second order all-pass sections which can be realized by two-port adaptors. They provide very desirable properties such as low sensitivity, high dynamic range and good stability even un der finite arithmetic conditions. Using the above mentioned filters as prototypes, a multirate approach is then introduced to deal with the design of fan filters with arbitrary angle and orientation, diamond an d elliptically-symmetric filters with arbitrary length of axes. Finall y, some design examples are given.