A universal characterization of maximum-entropy covariances for multidimensional signals is presented. It is shown that the maximum-entropy extension of an arbitrary partial covariance of a nonstationary multidimensional signal always has a banded inverse, i.e the inverse is sparse and has the same support as the given partial covariance. A dual formulation of the problem that makes it possible to approximate maximum-entropy extensions with models selected from suitably constrained model sets is introduced. It is proved that the best approximation in terms of multidimensional recursible autoregressive models can be determined by solving a set of linear equations. A simple graph-theoretic criterion is introduced to characterize those partial covariances whose maximum-entropy extension coincides with its autoregressive approximation, as in the conventional (one-dimensional stationary) maximum-entropy problem.>

A technique for performing exact calculations it discussed. The technique uses single-modulus P arithmetic to perform calculations over the finite field of integers and the finite ring of integers. It is shown that the arithmetic operations modulo P (which obviously can be impleinented in microprocessor configurations, VLSI, and/or software) can easily be extended from the range of values of the finite field of integers, modulo P, to the finite ring of integers, modulo pN where N is afny positive integer. This technique can be used for exact calculations over the rational numbers as well as complex numbers. Examples, block diagrams, And processor arrays are presented illustrating the simplicity of these operations.

Autoregressive lattice-filter modeling of two-dimensional fields is developed as an extension of one-dimensional lattice-filter theory. Several distinct methods of extension are presented, including a transfer function approach and a stochastic approach. The resulting lattice configurations span a wide range of structural complexity. They all exhibit the cascade structure of the conventional (one-dimensional) lattice-filter but differ widely in the structure of their elementary sections. It appears that orthogonality of prediction errors, which is essential for robust numerical behavior, requires high structural complexity. A configuration that offers a trade-off between perfect orthogonality and structural complexity is described.

A new approach for estimating the spectrum of two-dimensional fields from their autocorrelation matrix, based upon a recently developed autoregressive 2-D lattice parameter model, is presented.

The synthesis of lattice parameter digital filters from a given z-transform transfer function is considered. Included are several versions of AR, MA and ARMA structures. The approach is based upon partial fraction expansions and leads to numerical algorithms for parameter calculation which are numerically robust in terms of zero and poles close to the unit circle as well as self correcting for finite precision coefficients.

An efficient approach for direct form FIR filter implementation using microprocessor is presented. The approach uses the positive number and the coefficient partitioning techniques.

A unified approach to the efficient realization of FIR adaptive digital filters in both the time and frequency domains is presented. It is shown that previously published frequency domain implementations are contained within this unified approach. It is further shown that various combinations of implementations are possible, and that in working with data streams, care must be taken in using overlap-save and overlap-add sectioning procedures for proper frequency domain implementations.

New methods for designing digital lattice parameter all-pole (IIR) and all-zero (FIR) filters to meet a frequency response specification in a minimum least square error sense are presented.