Starting from a given polynomial, the Routh algorithm recursively gene
rates a family of all-pole transfer functions with the same energy of
the impulse response and a suitable number of its derivatives. It is s
hown that each of these energies is given by a linear combination of s
ome of the others according to the entries of a row of the Routh table
for the given polynomial. This fact can be exploited to evaluate cert
ain quadratic integrals in an efficient way.