On the Fourier coefficients with respect to the discrete Laguerre system

Abstract. The discrete Laguerre-functions play an important role in system identification. In this paper we investigate the Fourier coefficients with respect to the discrete Lagueerre system. Among others an explicit form is given for the Laguerre Fourier coefficients of rational functions. With the help of this formula we introduce a new transformation which can be used to reconstruct the pole of rational function. The domain of the transformation in question can be defined in the term of hyperbolic distance.