Design of Recursive Digital Filters in Parallel Form by Linearly Constrained Pole Optimization

We present a technique to iteratively optimize poles of a recursive digital filter in parallel form. Only exposing the poles as the variables to optimize, we employ a linearly constrained gradient descent routine in which the numerical estimation of the error gradient involves first obtaining the zeros by projecting the target response over a basis of responses defined by the pole positions at a given step. Example fits are presented for exponentially decaying white noise and measured violin radiativity filters.