Unstable digital filters and their equivalent stable filters

Unstable digital filters have divergent (or nonconvergent) z transforms. The Mellin integral representation of such series can be written down by inspection. A change in the path of integration gives the equivalent convergent series, and hence the stable filter. To carry out this procedure the analytic form of the original filter coefficients is required. If the analytic form is not known directly it may he possible to estimate it from a Domb-Sykes plot.