Multidimensional Frequency Response
IIR Filter Design

• Since the IIR filter-design problem is normally non-convex, designs for filters at neighboring parameter samples may end up at relatively different local minima

• `Small' changes in parameters may not correspond to `small' changes in filter coefficients

• Filter coefficients can thereby become discontinuous functions of parameters and therefore not interpolate well

• The interpolated filter coefficients may give a filter completely different from either of the statically designed filters it is interpolating between

• Design methods can add constraints to keep coefficients continuous in the parameters.
  • One method used the coefficients from a neighboring, already-designed point as the starting guesses for the design, which reduces the chances of ending up at a distant minimum.

• Importantly, there is no guarantee that the IIR filter will remain stable using interpolated coefficients, even if all the designed filters are stable

• Design methods that design to some stability margins can reduce the problem, at the cost of restricted possible designs

• Desired reponses with nearly unstable (``high-Q'') regions will be more prone to this problem (example: virtual analog VCF)

The datasets for multidimensional filter-design method can become very large, especially as the number of control parameters gets large