On the design of a broad class of 2-D recursive digital filters with fan, diamond and elliptically-symmetric responses

This paper deals with the design of a broad class of 2-D recursive digital filters including general fan, diamond and elliptically-symmetric filters. At first, the explicit design of quadrant and ±45° fan filters is reviewed. A full-plane diamond filter (both axes are nearly of length 2 π) can easily be obtained through an appropriate transformation of a ±45° fan filter. Using this diamond filter as a prototype, a very simple spectral transformation is then proposed to design full-plane circularly-symmetric filters (radius ≈π). 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 under 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 and elliptically-symmetric filters with arbitrary length of axes. Finally, some design examples are given