Simon Halvdansson
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View article: On a Time-Frequency Blurring Operator with Applications in Data Augmentation
On a Time-Frequency Blurring Operator with Applications in Data Augmentation Open
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical …
View article: Weyl Quantization of Exponential Lie Groups for Square Integrable Representations
Weyl Quantization of Exponential Lie Groups for Square Integrable Representations Open
We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question should admit at least one co-adjoint orbit of maximal possible dimension. The constr…
View article: Five ways to recover the symbol of a non-binary localization operator
Five ways to recover the symbol of a non-binary localization operator Open
Five constructive methods for recovering the symbol of a time-frequency localization operator with non-binary symbol are presented, two based on earlier work and three novel methods. For the two derivative methods which have previously bee…
View article: Measure-operator convolutions and applications to mixed-state Gabor multipliers
Measure-operator convolutions and applications to mixed-state Gabor multipliers Open
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition t…
View article: On a time-frequency blurring operator with applications in data augmentation
On a time-frequency blurring operator with applications in data augmentation Open
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical …
View article: On accumulated spectrograms for Gabor frames
On accumulated spectrograms for Gabor frames Open
Analogs of classical results on accumulated spectrograms, the sum of spectrograms of eigenfunctions of localization operators, are established for Gabor multipliers. We show that the lattice $\ell^1$ distance between the accumulated spectr…
View article: Measure-operator convolutions and applications to mixed-state Gabor multipliers
Measure-operator convolutions and applications to mixed-state Gabor multipliers Open
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition t…
View article: Quantum harmonic analysis on locally compact groups
Quantum harmonic analysis on locally compact groups Open
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…
View article: Five ways to recover the symbol of a non-binary localization operator
Five ways to recover the symbol of a non-binary localization operator Open
Five constructive methods for recovering the symbol of a time-frequency localization operator with non-binary symbol are presented, two based on earlier work and three novel methods. For the two derivative methods which have previously bee…
View article: Existence of uncertainty minimizers for the continuous wavelet transform
Existence of uncertainty minimizers for the continuous wavelet transform Open
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wa…
View article: Quantum harmonic analysis on locally compact groups
Quantum harmonic analysis on locally compact groups Open
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…
View article: Existence of Uncertainty Minimizers for the Continuous Wavelet Transform
Existence of Uncertainty Minimizers for the Continuous Wavelet Transform Open
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wa…
View article: Existence and Approximations of Optimal Wavelets
Existence and Approximations of Optimal Wavelets Open
In this thesis we consider two notions of mother wavelet uncertainty for the one-dimensional wavelet transform based on a new localization framework recently introduced by Levie and Sochen. It is shown that minimizers of these uncertaintie…