Homomorphic design of interpolated digital filters and equalisers

In this paper, interpolated digital filters, especially IFIR filters and interpolated allpasses, are designed in the quefrency domain. Systems with arbitrary behaviour in both log-magnitude response and phase response can be designed. Therefore, the methods are suitable for both selective filters and equalisers. A possibility is found to design the subfilters of an interpolated digital filter separately, one after another. It hence becomes possible to find the optimal filter orders for each subfilter quite quickly and easily. This method is then completed by a total filter optimisation. In both methods, the number of subfilters can be chosen freely, without any restrictions. Except for only one subfilter, this is also valid for the lengths of the delay lines in each subfilter. Further, a lemma is presented which yields an interesting insight into the efficiency of both IFIR filters and interpolated allpasses. A discussion about some drawbacks of homomorphic filter design completes the paper.