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

摘要

This paper deals with the design of a broad class of 2-D recursivendigital filters including general fan, diamond andnelliptically-symmetric filters. At first, the explicit design ofnquadrant and ±45° fan filters is reviewed. A full-planendiamond filter (both axes are nearly of length 2 Π) can easily benobtained through an appropriate transformation of a ±45° fannfilter. Using this diamond filter as a prototype, a very simple spectralntransformation is then proposed to design full-planencircularly-symmetric filters (radius ≈Π). These filters share thensame lattice wave digital structure and employ only first or secondnorder all-pass sections which can be realized by two-port adaptors. Theynprovide very desirable properties such as low sensitivity, high dynamicnrange and good stability even under finite arithmetic conditions. Usingnthe above mentioned filters as prototypes, a multirate approach is thennintroduced to deal with the design of fan filters with arbitrary anglenand orientation, diamond and elliptically-symmetric filters withnarbitrary length of axes. Finally, some design examples are given