Computable minimum lattice-like ARMA synthesis

A cascade synthesis for autoregressive moving-average (ARMA) digital filters, which uses the minimum number of delay elements (the degree of the transfer function in z), is described. The resulting structure results in the very convenient lattice from when the zeros of the transmission are not on the unit circle. The theory rests on conversion to scattering parameters and the use of a Richards' function, valid for complex zeros of rational functions with complex coefficients. Results of zeros of transmission on the unit circle are obtained by a parallel combination of lattices. By a suitable transformation, the sections are made computable while preserving the cascade form.<
>