On the inversion of singular operators

This paper is concerned with the inversion of digital singular convolution operators defined by a polynomial in the z-transform domain. For that purpose, in the one dimensional case (1D), the method given here proceeds by first approximating the polynomial by a rational transfer function, Which numerator results to be an autocorrelation functions, free of zeros on the unit circle. This is obtained by using the least square inverse concept of a polynomial. The extension to the 2D case, can be achieved using the well known 2D planar least square inverse polynomial (PLSI) in semicausal form. With this approach, the inversion deals with a non singular autocorrelation functions, so we can use the asymmtotical method given recently |1|.