A New Transform for the Stabilization and Stability Testing of Multidimensional Recursive Digital Filters

We present a new transform which, when applied to the denominator polynomial of the transfer function of an unstable multidimensional recursive digital filter (of a special class) will yield a stable polynomial with good preservation of the magnitude spectrum. In fact, the discrete Hilbert transform (DHT), used to stabilize 2-D and 1-D recursive digital filters, is a special case of the general multidimensional transform we present here. We also address the problem of stability testing of a multidimensional recursive digital filter and show that the new transform may be used to implement a straightforward test for stability of any causal multidimensional recursive digital filter, having no nonessential singularities of the second kind.