EXTENSIONS TO COMMON LAPLACE AND FOURIER-TRANSFORMS

The extended versions of common Laplace and Fourier transforms are giv en, This is achieved by defining a new function f(c)(p), p is an eleme nt of C related to the function to be transformed f(f), t is an elemen t of R, Then f(c)(p) is transformed by an integral whose path is defin ed on an inclined line on the complex plane, The slope of the path is the parameter of the extended definitions which reduce to common trans forms with zero slope. Inverse transforms of the extended versions are also defined, These proposed definitions, when applied to filtering i n complex ordered fractional Fourier stages, significantly reduce the required computation.