  Quantum singular value transformation (QSVT) enables the application of
polynomial functions to the singular values of near arbitrary linear operators
embedded in unitary transforms, and has been used to unify, simplify, and
improve most quantum algorithms. QSVT depends on precise results in
representation theory, with the desired polynomial functions acting
simultaneously within invariant two-dimensional subspaces of a larger Hilbert
space. These two-dimensional transformations are largely determined by the
related theory of quantum signal processing (QSP). While QSP appears to rely on
properties specific to the compact Lie group SU(2), many other Lie groups
appear naturally in physical systems relevant to quantum information. This work
considers settings in which SU(1,1) describes system dynamics and finds that,
surprisingly, despite the non-compactness of SU(1,1), one can recover a
QSP-type ansatz, and show its ability to approximate near arbitrary polynomial
transformations. We discuss various experimental uses of this construction, as
well as prospects for expanded relevance of QSP-like ans\"atze to other Lie
groups.
