Non-Separable Linear Canonical Wavelet Transform
H. M. Srivastava, Firdous A. Shah, Tarun Kumar Garg, Waseem Z. Lone, Huzaifa L. Qadri
Abstract
This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion of a non-separable linear canonical wavelet transform in L2(Rn). The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, we formulate several uncertainty inequalities, including the Heisenberg’s, logarithmic, and Nazorav’s inequalities for the proposed transform in the linear canonical domain. The obtained results are reinforced with illustrative examples.
Topics & Concepts
MathematicsOrthogonalityLogarithmWaveletContinuous wavelet transformApplied mathematicsWavelet transformSeparable spaceIntegral transformRange (aeronautics)Mathematical analysisDiscrete wavelet transformComputer scienceArtificial intelligenceGeometryComposite materialMaterials scienceMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsMachine Fault Diagnosis Techniques