Analysis of ill-conditioning of multi-channel deconvolution problems

Deconvolution of single- and multichannel systems is often an ill-conditioned problem whose exact solution boosts certain frequency bands excessively. Frequency-dependent regularisation can used to prevent this by attenuating sharp peaks in the magnitude response of the optimal filters. A z-domain analysis demonstrates that frequency-dependent regularisation works by pushing the poles of an ideal optimal solution away from the unit circle.