This article proposes a set of methodological steps that allows to address the problem of spectrum sensing in Cognitive Radio (CR) systems, allowing also to address the practical challenges involved in implementing this function; In the same way, the proposed methodological stages are validated through the formulation of a broadband spectrum sensing algorithm based on compressive sensing. The simulation results demonstrate that the proposed methodology allows to satisfy the development of spectrum sensing algorithms. These guarantee to satisfy the practical challenges considered in the process of development, allowing in this way to realize the spectrum sensing efficiently in function of the proposed sensate objective. It is evident that the sensing algorithm proposed using the formulated methodology has a better performance than other recently proposed algorithms.