TY - GEN

T1 - Uncertainty principles, minimum uncertainty samplings and translations

AU - Lantzberg, Daniel

AU - Lieb, Florian

AU - Stark, Hans Georg

AU - Levie, Ron

AU - Sochen, Nir

PY - 2012

Y1 - 2012

N2 - It has been shown recently, that the conventional variance based uncertainty measure associated with the wavelet transform can be arbitrarily small. Hence, no global minimizer exists. In this paper we introduce a new discretization scheme in scale and time shifts, such that the total uncertainty of a corresponding function system has the lowest possible value. We also describe a generalized uncertainty principle inspired by the familiar uncertainty principle in time-frequency analysis. As an example we apply this concept to wavelet analysis, leading to a new affine uncertainty principle. We also introduce waveforms minimizing this principle. Furthermore, we remark that the uncertainty measure associated with this new principle allows for decay estimates of the ambiguity function (reproducing kernel) associated with the wavelet transform.

AB - It has been shown recently, that the conventional variance based uncertainty measure associated with the wavelet transform can be arbitrarily small. Hence, no global minimizer exists. In this paper we introduce a new discretization scheme in scale and time shifts, such that the total uncertainty of a corresponding function system has the lowest possible value. We also describe a generalized uncertainty principle inspired by the familiar uncertainty principle in time-frequency analysis. As an example we apply this concept to wavelet analysis, leading to a new affine uncertainty principle. We also introduce waveforms minimizing this principle. Furthermore, we remark that the uncertainty measure associated with this new principle allows for decay estimates of the ambiguity function (reproducing kernel) associated with the wavelet transform.

KW - Uncertainty principle

KW - harmonic analysis

UR - http://www.scopus.com/inward/record.url?scp=84869816875&partnerID=8YFLogxK

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AN - SCOPUS:84869816875

SN - 9781467310680

T3 - European Signal Processing Conference

SP - 799

EP - 803

BT - Proceedings of the 20th European Signal Processing Conference, EUSIPCO 2012

T2 - 20th European Signal Processing Conference, EUSIPCO 2012

Y2 - 27 August 2012 through 31 August 2012

ER -