Approximation of stable linear systems via rational wavelets

The authors present a new approach to the approximation (and identification) of transfer functions of certain classes of stable linear systems using the theory of frames. Specifically they work with frames generated in H² (11⁺) by the action of the affine group on rational wavelets. It is well-known that the affine group Aff(1) and the group Sl(2) act on transfer functions via certain natural scaling processes. One such scaling action and some recent results of Daubechies are exploited to construct decompositions and approximations to transfer functions of infinite dimensional systems. A systematic computational method based on time-frequency concentrations has been developed to implement the ideas