Chebyshev polynomial based transfer functions for orthogonal lattice filters

A modification to the standard Schur algorithm is introduced. This is achieved by transforming the power series polynomials from the z domain to the Chebyshev polynomial domain. This transformation is performed using the mathematical formulae. The Schur algorithm is reformulated in the Chebyshev domain, and it is shown that this modified version has a similar complexity to the original version. The major advantage is that the accumulative computational round-off errors inherent in any Schur algorithm can be substantially reduced in the Chebyshev domain implementation. The Schur algorithm is used in many signal processing applications, and the potential for enhanced numerical stability of the reformulated method may offer substantial advantages with no increased computational overhead. It is shown that in some applications, such as the design of infinite impulse response lattice filters, the Chebyshev-based algorithm can make the difference between the method being practical and impractical.<
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