Para-Orthogonal Polynomials in Frequency Analysis

Abstract

this paper we shall sketch a di#erent approach to the frequency analysis problem, which uses zeros of para-orthogonal polynomials instead of zeros of orthogonal polynomials. A para-orthogonal polynomial is a polynomial of the form B n (#N , #, z) = # n (#N , z) + ## # n (# n , z), # T, (1.7) where # # n (z) = z # n (1/z) is the reversed polynomial. For convenience we shall suppress the # in all notation when we are considering a fixed value of # . The polynomial B n (#N , z) has n simple zeros z n , all lying on T. The following convergence result will be fundamental in the sequel. A proof can be found in [10]