We present a simple new analytical method for educing the materials' linear viscoelastic properties, over the widest range of experimentally accessible frequencies, from a simple step-strain measurement, without the need of preconceived models nor the idealization of real measurements. This is achieved by evaluating the Fourier transforms of raw experimental data describing both the time-dependent stress and strain functions. The novel method has been implemented into an open access executable "i-Rheo," enabling its use to a broad scientific community. The effectiveness of the new rheological tool has been corroborated by direct comparison with conventional linear oscillatory measurements for a series of complex materials as diverse as a monodisperse linear polymer melt, a bimodal blend of linear polymer melts, an industrial styrene-butadiene rubber, an aqueous gelatin solution at the gel point and a highly concentrated suspension of colloidal particles. The broadband nature of the new method and its general validity open the route to a deeper understanding of the material's rheological behavior in a variety of systems. (C) 2016 The Society of Rheology.