Use of the Nyquist Stability Criterion in the Design of Interactive Audio Digital Filters

Interactive audio processing systems sometimes include user-controlled digital filters, whose response is obtained by interpolating between different transfer functions. Audible artifacts produced by these filters are caused by migration across the unit circle of the zeros in their transfer function, depending on the interpolation parameter values. There are cases in which the Nyquist stability criterion for discrete-time systems can turn useful to inspect, and possibly modify the trajectories of such zeros. After a general discussion, two examples are illustrated in which Nyquist stability is used to optimize the response of filters realizing a linear interpolation between two transfer functions.