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). The most noticeable distinction of these polynomials with respect to the classical Meixner, Charlier, Hahn, and Krawtchouk DOP is dependence on only one parameter—the length of finite data. This makes them highly attractive for L-order blind fitting and analysis of informative processes. Properties of the UFIR polynomials are considered in detail along with the moments and recurrence relation. Examples of applications are given to blind approximation and phoneme pitch analysis.

► Unbiased finite impulse response (UFIR) functions are orthogonal.
► UFIR belongs to a one-parameter family of discrete orthogonal polynomials.
► UFIR polynomials can be used for blind approximation of finite data.
► UFIR polynomials perform better than the classical multi-parameter polynomials.
► Phoneme analysis and pitch tracking can be provided with UFIR polynomials.