  Disorder, ubiquitously present in realistic structures, is generally thought
to disturb the performance of analog wave devices, as it often causes strong
multiple scattering effects that largely arrest wave transportation. Contrary
to this general view, here, it is shown that, in some wave systems with
non-trivial topological character, strong randomness can be highly beneficial,
acting as a powerful stimulator to enable desired analog filtering operations.
This is achieved in a topological Anderson sonic crystal that, in the regime of
dominating randomness, provides a well-defined filtering response characterized
by a Lorentzian spectral line-shape. Our theoretical and experimental results,
serving as the first realization of topological Anderson insulator phase in
acoustics, suggest the striking possibility of achieving specific, non-random
analog filtering operations by adding randomness to clean structures.
