On the extension of the coupled fractional Fourier transform and its properties
Ramanathan Kamalakkannan, R. Roopkumar, Ahmed I. Zayed
Abstract
The coupled fractional Fourier transform is a two-dimensional fractional Fourier transform Fα,β that depends on two angles α,β that are coupled in such a way that the transform parameters are γ=(α+β)/2 and η=(α−β)/2. It generalizes the two-dimensional Fourier transform and it serves as useful tool in some applications in optics and signal processing. In this article we derive new properties of the transform, such as its additive property. We then extend some of them to L2(R2) and show that the transform is a unitary operator on L2(R2).
Topics & Concepts
Fractional Fourier transformHartley transformMathematicsFourier transformDiscrete Fourier transform (general)Extension (predicate logic)Harmonic wavelet transformNon-uniform discrete Fourier transformS transformFourier transform on finite groupsShort-time Fourier transformUnitary stateMathematical analysisFourier analysisComputer scienceWavelet transformArtificial intelligenceDiscrete wavelet transformWaveletPolitical scienceWavelet packet decompositionProgramming languageLawMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation