Software Radio has been proposed in the 1990s as the solution to flexible transceiver design for future wireless systems. Potential advantages and drawbacks of this approach have been described and analysed in verbose format in many articles. However, a mathematical perspective of the software radio design problem is to be found in the literature only once. Despite this attempt to develop a sound formal description the conclusions do not reach beyond algorithm design. Open issues in system design are often mentioned, but remain unresolved hitherto. We develop a novel mathematical perspective of software radio, and we formulate the design problem accordingly, by means of an integer linear programming (ILP) representation. This type of problem is well-known in computer science and operations research, but it has never been linked to software radio design before. In a first approach to solve the ILP problem we reduce it to a scheduling problem with processor constraints. In the remainder of the theoretical section we introduce the notions of granularity G and speedup s to assess the quality of modular implementations. A random runtime argument leads the way to a system-theoretic approach to modular design issues such as maximizing speedup over a great number of different implementations. For the special case G = 1 we deduce the speedup potential of a primitive graph in analytical form. In the experimental section we compare simulation results to our theory, and we extend the experiments to a more complicated graph which stems from a real software radio design project. The paper concludes with a discussion and a brief outlook to future research issues.