Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles
Mawardi Bahri
Abstract
Abstract The windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.
Topics & Concepts
Fourier transformFractional Fourier transformOrthogonalityMathematicsHartley transformRelation (database)Transformation (genetics)Fourier transform on finite groupsDiscrete Fourier transform (general)Mathematical proofConstant Q transformHarmonic wavelet transformMathematical analysisShort-time Fourier transformFourier analysisComputer scienceArtificial intelligenceWavelet transformGeometryData miningGeneBiochemistryChemistryWaveletDiscrete wavelet transformMathematical Analysis and Transform MethodsDigital Filter Design and ImplementationImage and Signal Denoising Methods