A property of the Routh table and its use

Starting from a given polynomial, the Routh algorithm recursively generates a family of all-pole transfer functions with the same energy of the impulse response and a suitable number of its derivatives. It is shown that each of these energies is given by a linear combination of some 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 certain quadratic integrals in an efficient way.<
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