Orthogonal realization of first-order allpass filters for two-dimensional signals

An orthogonal realization for two-dimensional first-order strictly-stable allpass transfer functions is presented. It consists of two shift (delay) elements (one for each dimension) and three two-input/two-output memory-less lossless cells (i.e., elementary orthogonal rotations). We establish a one-to-one correspondence between the parameters of our orthogonal realization and those of the corresponding transfer function. A brief discussion of finite precision effects on our realization and a comparison with previous realizations are also included.

[1]  M. Morf,et al.  New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality , 1977, Proceedings of the IEEE.

[2]  Sanjit K. Mitra,et al.  Passivity properties of low-sensitivity digital filter structures , 1985 .

[3]  Chikkannan Eswaran,et al.  Minimal multiplier realization of 2-D all-pass digital filters , 1988 .

[4]  Harpreet Singh,et al.  First-order 2-D all-pass network realization , 1981 .

[5]  Panajotis Agathoklis,et al.  Criteria for the absence of limit cycles in two-dimensional discrete systems , 1984 .

[6]  M. Sudhakara Reddy,et al.  Realization of first-order two-dimensional all-pass digital filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[7]  Donald D. Givone,et al.  Minimization of Multidimensional Linear Iterative Circuits , 1973, IEEE Transactions on Computers.

[8]  Thomas S. Huang,et al.  Stability of two-dimensional recursive filters , 1972 .

[9]  V. Ganapathy,et al.  Minimal delay realization of first order 2-D all-pass digital filters , 1983 .

[10]  Thomas Kailath,et al.  Orthogonal digital filters for VLSI implementation , 1984 .

[11]  N. El-Agizi,et al.  Two-dimensional digital filters with no overflow oscillations , 1979 .

[12]  Sun-Yuan Kung,et al.  New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness , 1977, Proceedings of the IEEE.

[13]  N. Bose.  Applied multidimensional systems theory , 1982 .

[14]  M.N.S. Swamy,et al.  Comments on "Minimal multiplier realization of 2-D all-pass digital filters" by K. Manivannan and C. Eswaran , 1989 .

[15]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.