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In this paper we are discussing various aspects of wavelet filters. Whilethere are earlier studies of these filters as matrix valued functions inwavelets, in signal processing, and in systems, we here expand the framework.Motivated by applications, and by bringing to bear tools from reproducingkernel theory, we point out the role of non-positive definite Hermitian innerproducts (negative squares), for example Krein spaces, in the study ofstability questions. We focus on the non-rational case, and establish newconnections with the theory of generalized Schur functions and their associatedreproducing kernel Pontryagin spaces, and the Cuntz relations.

Extending wavelet filters. Infinite dimensions, the non-rational case, and indefinite-inner product spaces