The special relativistic (space-time) Fourier transform (SFT) in the Clifford space-time algebra $Cl_{(3;1)}$ can be considered as an extension of the Quaternionic Fourier transform. The aim of this contribution is twofold. First, it will seek to outline some important properties of the SFT such as the continuity and Plancherel identity. Second, to establish the associated Heisenberg and Hardy's uncertainty principles by means of the space-time split.