Two-dimensional filters with wideband circularly symmetric frequency response

Two-dimensional filters with circularly symmetric frequency response find application in isotropic filtering of images. An effective method for designing this class of filters is based on applying the McClellan transformation to a one-dimensional prototype. The requirement of wideband circular symmetry necessitates the use of high-order generalized McClellan transformations, where the transformation has to be redesigned as the passband radius increases. In this paper a simple procedure for designing wideband two-dimensional FIR filters with circular symmetry is presented. The procedure is based on combining the low-order original McClellan frequency transformation with a decimation of the resulting 2-D filter impulse response. Conditions to be met by the one-dimensional prototype filter are derived along with the minimum decimation factor required in the design. For given specifications with circular symmetry, it is shown that a solution can always be derived using the fixed low-order transformation. >

[1]  M. Swamy,et al.  Design of circularly symmetric two-dimensional FIR digital filters employing transformations with variable parameters , 1983 .

[2]  R. M. Mersereau,et al.  McClellan transformations for two-dimensional digital filtering-Part I: Design , 1976 .

[3]  George V. Moustakides,et al.  Design of two-dimensional zero-phase FIR filters via the generalized McClellan transform , 1991 .

[4]  Thomas S. Huang,et al.  Two-dimensional digital signal processing I. Linear filters. , 1981 .

[5]  Jae S. Lim,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[6]  R. Mersereau,et al.  The design of arbitrary 2-D zero-phase FIR filters using transformations , 1980 .

[7]  Mark J. T. Smith,et al.  A filter bank for the directional decomposition of images: theory and design , 1992, IEEE Trans. Signal Process..

[8]  M. Swamy,et al.  Formulas for parameter scaling in the McClellan transform , 1986 .

[9]  F. Mintzer,et al.  The design of optimal multirate bandpass and bandstop filters , 1978 .

[10]  Dan E. Dudgeon,et al.  Multidimensional Digital Signal Processing , 1983 .

[11]  M.N.S. Swamy,et al.  Scaling-free McClellan transform for 2-D digital filters , 1985 .

[12]  Thomas S. Huang,et al.  Two-Dimensional Digital Signal Processing I , 1981 .

[13]  D H Tay,et al.  Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables , 1993, IEEE Trans. Image Process..

[14]  L. Rabiner,et al.  A novel implementation for narrow-band FIR digital filters , 1975 .