Generalized feedforward filters with complex poles

The authors propose an extension to an existing structure, the gamma filter, replacing the real pole on the tap-to-tap transfer function with a pair of complex conjugate poles and a zero. The new structure is, like the gamma filter, an IIR filter with restricted feedback whose stability is trivial to check. While the gamma filter decouples the memory depth from the filter order for low-pass signals, the proposed structure decouples the memory depth and the central frequency from the filter order for band-pass signals. The learning equations of the model parameters are presented and shown to introduce an additive O(p) complexity to the backpropagation algorithm, where p is the filter order. The error surface for a linear filter is investigated in a system identification context, and the presence of local minima is confirmed. The performance of the proposed model was found to be better than that of the time-delay neural net in a nonlinear system identification context