2024/05/20 by Karlheinz Gröchenig, Gröchenig, Karlheinz, Irina Shafkulovska +1 · 2 citations
Engineering · #Fault Detection and Control Systems #Structural Health Monitoring Techniques #Control Systems and Identification
paper · pdf · doi:10.48550/arxiv.2405.12112
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which metaplectic Wigner distributions satisfy an uncertainty principle in the style of Benedicks and Amrein-Berthier. That is, if the metaplectic Wigner distribution is supported on a set of finite measure, must the functions then be zero? While this statement holds for the short-time Fourier transform, it is false for some other natural time-frequency representations. We provide a full characterization of the class of metaplectic Wigner distributions which exhibit an uncertainty principle of this type, both for sesquilinear and quadratic versions.