On the solutions of the rational covariance extension problem corresponding to pseudopolynomials having boundary zeros

In this paper, we study the rational covariance extension problem when the chosen pseudopolynomial of degree at most n has zeros on the boundary of the unit circle. In particular, we derive a necessary and sufficient condition for a solution to be bounded (i.e. has no poles on the unit circle). Furthermore, we propose a new procedure for computing all bounded solutions for this special case of zeros of pseudopolynomials on the boundary and illustrate it by means of two examples.