Routh´s like array for the zero location of continuous- and discrete-time filters

Routh´s table for determining the zero location of a polynomial with respect to the imaginary axis is generalized and presented without distinction between the real and complex cases. The new table is then transposed to the z-domain. It is shown that this transposition gives, in particular, the classical tables computed by processes based on the three-term recursion of polynomials. This generalization is used to solve the problem of classical singularities appearing in the study of the zero location of a polynomial with respect to the imaginary axis or to the unit circle. It also makes clear the connections existing between the classical methods