Toward to Recurrent Form of the Impulse Response of UFIR Filters

In this paper, we present a new scheme to determining the impulse response function using the recursive relation in the Unbiased Finite Impulse Response (UFIR) filters. The theory of Discrete Orthogonal Polynomials (DOP) is considered here to modify the classical polynomials such as Shmaliy polynomials using the weighted norm and the probability density function (PDF), respectively. Beginning of the three-term recurrence relation and transforming the problem of the development of the impulse response function in the UFIR filter. Finally, we include two appendices within which we demonstrate the equivalence between the traditional method that uses a matrix process and the other that employs the recurrent form; in both cases we put n = 1, for an impulse response of the ramp gain in UFIR filter.