g and g2 can be eliminated from the previous equations, which leads to the necessary condition:
For filite impulse response filters, the Fourier transforms of such filters are trigonometric polynomials, and conditions (7.121) and (7.129) can be interpreted as Bezout identities in the ring of trigonometric polynomials. In this ring, units are trigonometric monomials. Equations (7.121) - (7.122) form a linear system with respect to h2 and g2, and it can be shown that the associated matrix is unimodular, i.e., its determinant is a trigonometric monomial. then there exists a real number a and an integer l such that
