Abstract
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).DOI: http://dx.doi.org/10.5755/j01.eee.120.4.1449
Highlights
Filter theory represents one of the strictest disciplines with the possibilities of applications in various frequency ranges and technologies [1,2,3,4]
New class explicit filter functions for continuous signals generated by the classical Christoffel-Darboux formula for classical Jacobi and Gegenbauer orthonormal polynomials are described in detail [10, 11]
This paper presents an original approach to linear phase two-dimensional finite impulse response (FIR) digital filter design yielding significant improvements
Summary
Filter theory represents one of the strictest disciplines with the possibilities of applications in various frequency ranges and technologies [1,2,3,4]. New class explicit filter functions for continuous signals generated by the classical Christoffel-Darboux formula for classical Jacobi and Gegenbauer orthonormal polynomials are described in detail [10, 11]. There have been a number of attempts to solve the complex problem of generating linear phase two-dimensional finite impulse response (FIR) digital filters of lower order, e.g. A new class of the linear phase two-dimensional FIR digital filters generated by the proposed formula is given
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