Uncertainty principle corresponding to an orthonormal wavelet system
In this article, we first investigate a finite collection of functions in that satisfies some
localization properties in a region of the time–frequency plane. For this, a group theoretic
approach based on the complete digit set associated to an invertible matrix is used. It leads
to the construction of an orthonormal wavelet system (ONWS) which is concentrated in time
as well as frequency. We study and characterize the ONWS. Further, some results on the
uncertainty principle corresponding to the ONWS are obtained.
localization properties in a region of the time–frequency plane. For this, a group theoretic
approach based on the complete digit set associated to an invertible matrix is used. It leads
to the construction of an orthonormal wavelet system (ONWS) which is concentrated in time
as well as frequency. We study and characterize the ONWS. Further, some results on the
uncertainty principle corresponding to the ONWS are obtained.
In this article, we first investigate a finite collection of functions in that satisfies some localization properties in a region of the time–frequency plane. For this, a group theoretic approach based on the complete digit set associated to an invertible matrix is used. It leads to the construction of an orthonormal wavelet system (ONWS) which is concentrated in time as well as frequency. We study and characterize the ONWS. Further, some results on the uncertainty principle corresponding to the ONWS are obtained.
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