A new class of discrete orthogonal polynomials for blind fitting of finite data

We show that the polynomial unbiased finite impulse response (UFIR) functions derived by Shmaliy establish a new class of a one-parameter family of discrete orthogonal polynomials (DOP). Unlike the classical finite-data DOP, the UFIR polynomials depend on only one parameter - the length of finite data. This makes them highly attractive for L-order blind fitting and representation of informative processes. Examples of applications are given for voice phoneme analysis and approximation in a comparison with the Hahn´s polynomials.