Christoffel-Darboux Formula Most Directly Applied in Generating Economical Linear Phase Low-Pass Digital FIR Filter Functions
Keywords:Difference equations, digital filters, filtering theory, finite impulse response filter
AbstractThe approximation problem of a filter function of even and odd order is solved mathematically in this paper most directly applying the proposed Christoffel-Darboux formula for two continual orthogonal polynomials on the equal finite segment. As a result, a linear phase digital finite impulse response (FIR) filter function is generated in compact explicit form. In addition, a new difference equation and structure of linear phase digital FIR filter are proposed. Two examples of the extremely economic FIR filter (with four adders and without multipliers) designed by the proposed technique are presented. The proposed solutions are extremely efficiency in regard to energy consumption.
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