Adjoint Operators of Fourier-Finite Mellin Transform

Abstract Transform analysis of generalized functions concentrates on finite parts of integrals, generalized function and distributions. The Fourier- Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function. A specific form of the Mellin transform, referred to as the “scale transform”, is known to be a natural complement to the Fourier transform for wideband analytic signals. While the Fourier-Finite Mellin has found numerous applications in optical pattern recognition, ship classification by sonar and radar and image processing. These Fourier and Finite Mellin transforms have various properties and these properties have various applications in many fields. The main purpose of this paper is to describe the Adjoint operators of Fourier-Finite Mellin transform.