Temporal stability of N-dimensional linear processors and its applications

The transfer function of an
N
-dimensional linear processor is the double-ended
\overrightarrow{z}
-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
\overrightarrow{z}
, 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.