On the numerical conditioning in orthogonal filters

Orthogonal embedding filters are defined in terms of the numerical conditioning of the realization matrix which describes the state-update and output computations in a digital filter. The construction of an orthogonal embedding filter consists of embedding a desired transfer function into a multivariable all-pass system which is implemented by an orthogonal realization matrix. The embedding system is ideally conditioned, and the numerical conditioning of the partial transfer realization matrix of interest is addressed. The numerical conditioning of the partial transfer realizations in orthogonal embedding filters is examined. Additionally, the partial transfer realizations are related to the class of generalized orthogonal state variable filters, or principle axis realizations which are defined in terms of the statistical properties of the state variables