As the constructible counterpart of the Fourier-Mukai transformation, the non-abelian Mellin transformation of a constructible complex can be considered as taking the hyper-cohomology of the complex twisted by all possible local systems simultaneously. We will explain a t-exactness result about the non-abelian Mellin transformation, generalizing a theorem of Gabber-Loeser on affine torus. We will also discuss some local vanishing properties of the Sabbah's specialization functor, which is a key step in the proof of the t-exactness result.