Modulation spaces as a smooth structure in noncommutative geometry

Abstract We demonstrate how to construct spectral triples for twisted group $$C^*$$ C? -algebras of lattices in phase space a second-countable locally compact abelian using class weights appearing time–frequency analysis. This yields way constructing quantum $$C^k$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Ck -structures on Heisenberg modules, and we show obtain such structures Gabor analysis certain weighted analogues Feichtinger’s algebra. treat the standard triple noncommutative 2-tori as special case, another example define solenoids -structure associated modules.