Uncertainty Principles for Rényi Entropy Under Continuous and Discrete Quaternion Fourier Transforms
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DOI: 10.1002/mma.70265
Abstract: We first prove the sharp Hausdorff–Young inequality for the right‐sided continuous quaternion Fourier transform (RCQFT), and the Hausdorff–Young inequalities for the discrete quaternion Fourier transform (DQFT) and for the quaternion Fourier series (QFS), respectively. Next,… read more here.
Keywords: uncertainty principles; quaternion fourier; nyi entropy; discrete quaternion ... See more keywords
A Variation on Inequality for Quaternion Fourier Transform, Modified Convolution and Correlation Theorems for General Quaternion Linear Canonical Transform
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DOI: 10.3390/sym14071303
Abstract: The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform… read more here.
Keywords: quaternion linear; quaternion; transform; linear canonical ... See more keywords
Two-Dimensional Quaternion Fourier Transform Method in Probability Modeling
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DOI: 10.3390/sym16030257
Abstract: The Fourier transform plays a crucial role in statistics, applied mathematics, and engineering sciences. In this study, we give a definition of the two-dimensional quaternion Fourier transform, which is an extension of the two-dimensional Fourier… read more here.
Keywords: quaternion fourier; two dimensional; fourier transform; dimensional quaternion ... See more keywords