Study of the stability and other properties of a class of second order variable magnitude 2-D digital transfer functions with 2-parameter denominator

This paper considers a 2-D transfer function of second order in each variable containing two real parameters. The conditions that the two parameters have to satisfy in order to obtain stable transfer functions are determined. It is shown that the four basic filters, low-pass, high-pass, band-pass and band-elimination, can be obtained. Different types of contours and magnitude responses for each of these filters can be generated by suitably varying the two parameters.