Scientific paper ID 223 : 2008/2

A new window function, obtained from algebraic polynomial, approximating delta function in Hausdorff.s metric is presented in the article. Equations defining polynomial parameters are shown. A domain of definition and analytical equations for Hausdorff.s window function are defined. The change of Hausdorff.s window due to the Hausdorff.s distance and power of polynomial is graphically presented. Based on the obtained relations, a methodic for digital FIR filter synthesis is offered. Equations for impulse and frequencies response are defined. Relations defining filter order and Hausdorff.s distance, depending on the attenuation in stop band and the value of transition length, are presented. An example for filter synthesis is shown. Comparative analysis of magnitude responses of Hausdorff and Kaiser.s FIR filters is demonstrated