A new transform for the stabilization and stability testing of multidimensional recursive digital filters
H. Damera-Venkata, Mukundan Venkataraman, M.S. Hrishikesh, P.S. Reddy · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · 2000
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.