This document presents a comprehensive solution to a computer science assignment, addressing key concepts such as the sampling theorem, 16-QAM modulation, Shannon's equation, refractive index, and radiofrequency analysis. The solution includes detailed calculations for determining bit rates and minimum bandwidth, a signal constellation diagram for 16-QAM, and explanations of Shannon's theorem. It also covers multimode distortion, dispersion, attenuation in optical fibers, and the differences between Fourier series and Fourier transforms. Furthermore, the assignment delves into radiofrequency analysis, including frequency allocation and radio propagation mechanisms within the ionosphere. The document provides diagrams, calculations, and explanations to aid in understanding these complex topics.