Optimality conditions for a specific class of truncated Kautz series

Kautz functions constitute a basis in L/sup 2/ and can be used for filter synthesis starting from a prescribed transient response. In a practical situation, only truncated series are used and thus the speed of convergence of such series is of importance. This convergence speed is a function of the parameters. The Kautz functions that are considered can be generated by a line of identical Nth-order allpass sections. The optimality conditions for the parameters of this specific class of truncated Kautz series are established solely on the basis of the orthonormality and the polynomial character of the basis functions.