Linear Phase Two-Dimensional FIR Digital Filter Functions Generated by applying Christoffel-Darboux Formula for Orthonormal Polynomials

  • D. G. Ciric University of Niš
  • V. D. Pavlovic University of Niš


Global Christoffel-Darboux formula for four orthonormal polynomials on two equal finite segments for generating linear phase two-dimensional finite impulse response (FIR) digital filter functions in a compact explicit representative form is proposed in this paper. The formula can be most directly applied for solving mathematically the approximation problem of a filter function of even and odd order. An example of a new class extremely economic linear phase two-dimensional FIR digital filter without multipliers obtained by the proposed approximation technique is presented. The generated linear phase two-dimensional FIR filter functions have two symmetries, that is, the following relations are valid: H(z1,z2)=H(z2,z1) and H(z1,z2)=H(-z1,-z2)  and . Ill. 3, bibl. 15 (in English; abstracts in English and Lithuanian).