Temporal stability of N-dimensional linear processors and its applications

The transfer function of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -dimensional linear processor is the double-ended <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{z}</tex> -transform of its impulse response function. Every rational transfer function has a unique, stable expansion if the denominator polynomial is nonzero on the unit circle product subspace of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{z}</tex> , and can be realized by a frame recursive processing scheme. As an extension of the above the present paper stated and proved the conditions for an active infinite network to be stable both spatially and temporally.