New results concerning stability of multidimensional digital filters

This thesis introduces three new fundamental results concerning stability of digital filters.;It is well known that in order for a 2-D digital filter to be BIBO stable, it is necessary that the denominator of the real rational filter transfer function is a discrete scattering Hurwitz polynomial (DSHP). A very simple concept for a test procedure for 2-D DSHP is presented first. The concept is based on the definition of the stability threshold (stability margin) and of the geometrical properties of the root loci of the polynomial under the test. Polynomials with a finite number of simple zeros on ;The second result deals with a very special class of m-D (m ;Finally, a new contribution to the very old, but still vital problem of the determination of the upper bound for polynomial zeros is given. The newly introduced bound is obtained through the application of Cauchy's bound theorem to a new polynomial, which is derived from the original one by way of an exponential transform.