Approximation of two-variable filter specifications in analog domain

This paper describes a technique for approximating 2-variable filter specifications in the continuous or analog domain. It is shown that the design of 2-variable filter functions using this approach reduces to the problem of identifying a suitable 2-variable reactance function g(s_1,s_2) and the realization of a stable single-variable transfer function T(s) . Then T(g(s_1,s_2)) is the desired 2-variable stable transfer function which is guaranteed to have at least one realization whenever T(s) and g(s_1,s_2) are realizable. Applications of the theory developed in this paper are presented in the design of lumped-distributed filters and 2-dimensional digital filters.

[1]  E. Jury,et al.  Spectral transformations for two-dimensional digital filters , 1976 .

[2]  L. Rabiner,et al.  Design techniques for two-dimensional digital filters , 1972 .

[3]  J. D. Rhodes,et al.  Driving-Point Synthesis of Resistor-Terminated Cascades Composed of Lumped Lossless Passive 2-ports and Commensurate TEM Lines , 1972 .

[4]  Kenneth Steiglitz.  The Equivalence of Digital and Analog Signal Processing , 1965, Inf. Control..

[5]  P.I. Richards,et al.  Resistor-Transmission-Line Circuits , 1948, Proceedings of the IRE.

[6]  J. D. Rhodes,et al.  Explicit solution for the synthesis of two-variable transmission-line networks , 1973 .

[7]  J. Lodge,et al.  A note on "An lp design technique for two-dimensional digital recursive filters" , 1978 .

[8]  G. Maria,et al.  An l p design technique for two-dimensional digital recursive filters , 1974 .

[9]  T. Huang,et al.  Two-dimensional windows , 1972 .

[10]  Ahmed M. Soliman,et al.  Synthesis of a class of multivariable positive real functions using Bott-Duffin technique , 1971 .

[11]  S. Treitel,et al.  Stability and synthesis of two-dimensional recursive filters , 1972 .

[12]  T. Kasami,et al.  Positive Real Functions of Several Variables and Their Applications to Variable Networks , 1960 .

[13]  Ernest L. Hall.  A comparison of computations for spatial frequency filtering , 1972 .

[14]  Isao Shirakawa,et al.  Synthesis of Some Classes of Multivariable Cascaded Transmission-Line Networks , 1968 .

[15]  J. Rhodes,et al.  Cascade synthesis of transmission lines and lossless lumped networks , 1971 .

[16]  M. Fahmy,et al.  l_p approximation of the group delay response of one- and two-dimensional filters , 1974 .

[17]  H. Ansell.  On Certain Two-Variable Generalizations of Circuit Theory, with Applications to Networks of Transmission Lines and Lumped Reactances , 1964 .

[18]  M. Uruski,et al.  Synthesis of a network containing a cascade of commensurate transmission lines and lumped elements , 1972 .

[19]  J. Delansky.  Some synthesis methods for adjustable networks using multivariable techniques , 1969 .

[20]  T. W. Parks,et al.  EQUIRIPPLE APPROXIMATION OF FAN FILTERS , 1972 .

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

[22]  A. Venetsanopoulos,et al.  Design of circularly symmetric two-dimensional recursive filters , 1974 .

[23]  Douglas R. Goodman,et al.  Some stability properties of two-dimensional linear shift-invariant digital filters , 1977 .

[24]  T. Koga,et al.  Synthesis of Finite Passive n-Ports with Prescribed Two-Variable Reactance Matrices , 1966 .

[25]  T. Koga,et al.  Synthesis of Finite Passive n-Ports with Prescribed Positive Real Matrices of Several Variables , 1968 .

[26]  Realizability of a Resistively Terminated Cascade of Lumped Two-Port Networks Separated by Noncommensurate Transmission Lines , 1967, IEEE Transactions on Circuit Theory.

[27]  Y. Oono,et al.  Synthesis of a Variable-Parameter One-Port , 1963 .

[28]  T. N. Rao.  Minimal synthesis of two-variable reactance matrices , 1969 .

[29]  Y. Kamp,et al.  Maximally flat nonrecursive two-dimensional digital filters , 1974 .

[30]  T. Koga.  Synthesis of a resistively terminated cascade of uniform lossless transmission lines and lumped passive lossless two-ports , 1971 .

[31]  R. M. Mersereau,et al.  An Efficient Algorithm for the Design of Equiripple Two-Dimensional FIR Digital Filters. , 1975 .