14 citations · 27 across the 13 of their papers we have counts for
10 papers · 1 filter
Gabor Frames of Totally Positive Functions: A Complete Characterization
Jaume de Dios Pont, Karlheinz Gröchenig, Lukas Liehr +2
We prove that the set of time-frequency shifts with a continuous, integrable totally positive function and lattice parameters $α…
Stability in unlimited sampling
José Luis Romero, Irina Shafkulovska
Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of band…
A Characterization of Metaplectic Time-Frequency Representations
Karlheinz Gröchenig, Irina Shafkulovska
We characterize all time-frequency representations that satisfy a general covariance property: any weak*-continuous bilinear mapping that intertwines time-frequency shifts on the c…
More Uncertainty Principles for Metaplectic Time-Frequency Representations
Karlheinz Gröchenig, Irina Shafkulovska
We develop a method for the transfer of an uncertainty principle for the short-time Fourier transform or a Fourier pair to an uncertainty principle for a sesquilinear or quadratic…
Benedicks-type uncertainty principle for metaplectic time-frequency representations
Karlheinz Gröchenig, Irina Shafkulovska
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigne…
On the frame property of Hermite functions and exploration of their frame sets
Markus Faulhuber, Irina Shafkulovska, Ilya Zlotnikov
We study Gabor frames with Hermite window functions. Gröchenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety…
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig, Irina Shafkulovska
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a…
The metaplectic action on modulation spaces
Hartmut Führ, Irina Shafkulovska
We study the mapping properties of metaplectic operators on modulation spaces of the type . Our main r…
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
Philipp Grohs, Lukas Liehr, Irina Shafkulovska
We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove…
Gabor frame bound optimizations
Markus Faulhuber, Irina Shafkulovska
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the squar…