## The complex Kautz filter

Figure: the general (complex) Kautz filter consists of an all-pass backbone, and all-pole tap-output filters, with corresponding normalization terms. The tap-output filter and the subsequent all-pass block are coupled, as can be seen. FIR and Laguerre filters are special cases of the Kautz filter, with all poles at z=0 or z=a, -1<a<1, respectively.
The complex Kautz filter is completely determined by a set of poles and the filter weights:

The Matlab function **S**=compkautz(**a**,M,**x**) produces (length M) responses to input vector **x**. The response of the filter is then the matrix product **y**=**S*****w**. The filter order is (defined to be) N=length(**a**).