84,900 research outputs found
Time-Frequency Shift Invariance of Gabor Spaces with an -Generator
We consider non-complete Gabor frame sequences generated by an -function
and a lattice and prove that there is such that
all time-frequency shifts leaving the corresponding Gabor space invariant have
their parameters in . We also investigate time-frequency
shift invariance under duality aspects
The Consumer’s Stake in the Finance Company Code Controversy
The duality between time and frequency domain methods for linear systems is well known. It plays a crucial role for example in control systems design, and the domains are thought of complementing rather than competing. Quite recently, the full interplay and duality between the two domains have been clear also in system identification applications. In this contribution, this duality is discussed. The emphasis is on how it can be used to create a software environment for linear system identification that is as transparent as possible with respect to the data domains
Co-compact Gabor systems on locally compact abelian groups
In this work we extend classical structure and duality results in Gabor
analysis on the euclidean space to the setting of second countable locally
compact abelian (LCA) groups. We formulate the concept of rationally
oversampling of Gabor systems in an LCA group and prove corresponding
characterization results via the Zak transform. From these results we derive
non-existence results for critically sampled continuous Gabor frames. We obtain
general characterizations in time and in frequency domain of when two Gabor
generators yield dual frames. Moreover, we prove the Walnut and Janssen
representation of the Gabor frame operator and consider the Wexler-Raz
biorthogonality relations for dual generators. Finally, we prove the duality
principle for Gabor frames. Unlike most duality results on Gabor systems, we do
not rely on the fact that the translation and modulation groups are discrete
and co-compact subgroups. Our results only rely on the assumption that either
one of the translation and modulation group (in some cases both) are co-compact
subgroups of the time and frequency domain. This presentation offers a unified
approach to the study of continuous and the discrete Gabor frames.Comment: Paper (v2) shortened. To appear in J. Fourier Anal. App
A Classical String in Lifshitz-Vaidya Geometry
We study the time evolution of the expectation value of a rectangular Wilson
loop in strongly anisotropic time-dependent plasma using gauge-gravity duality.
The corresponding gravity theory is given by describing time evolution of a
classical string in the Lifshitz-Vaidya background. We show that the
expectation value of the Wilson loop oscillates about the value of the static
potential with the same parameters after the energy injection is over. We
discuss how the amplitude and frequency of the oscillation depend on the
parameters of the theory. In particular, by raising the anisotropy parameter,
we observe that the amplitude and frequency of the oscillation increase.Comment: 19 pages, 5 figure
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