Introduction To Fractional Fourier-Laplace Transform

The Linear Canonical transform is four parameterized integral transform, which is an important tool in signal processing and optics. The application of linear canonical transform in quantum mechanics has focused attention on its complex extension. Fractional Laplace transform is special case of complex linear canonical transform. Fractional Fourier transform emerged as an extension of the Fourier transform. This paper presents introduction to fractional Fourier-Laplace transform. Here the definition of generalized fractional Fourier-Laplace transform is proposed. Different properties of kernel are discussed. The Inversion formula for Fractional Fourier-Laplace transform (FrFLT) is proved. Keywordsâ€” Fractional Fourier Transform, Fractional Laplace Transform, Generalized Function, Testing Function Space, Signal Processing.