where x { κ κ } = 1 κ κ a r c s i n h ( κ κ x ) and ω ω { κ κ } = 1 κ κ a r c s i n h ( κ κ ω ω ) . The κ-Fourier transform imposes an asymptotically log-periodic behavior by deforming the parameters x and ω ω in addition to a damping factor, namely 1 + κ κ 2 x 2 .