Optimal parameters in Laguerre and Kautz series

In the context of parsimonious signal and systems representation Laguerre and Kautz series are considered. Arbitrary causal signals having finite energy can be represented in a Laguerre or Kautz series. The Laguerre and Kautz series depend on a single free parameter. In the Laguerre series the parameter represents a pole of the transfer function. The usual Laguerre series evolves when this pole is real-valued. A good parameter choice in the sense of a compaction of the energy in the first terms of the series can then be made on the basis of a few simple signal measurements. It is shown that this also holds for a Laguerre series having a complex-valued pole. This result is subsequently used to estimate the optimal poles for a Kautz series having a repeated complex-conjugated pole pair.