On the application of asymptotically equivalent sequences of matrices to the derivation of the continuous time Gaussian channel capacity

Based on the concept of Asymptotically Equivalent sequences of matrices, this article derives in simple terms the classical expression for the capacity of the continuous-time filtered channel with additive colored Gaussian noise. We follow the direct approach of over-sampling the continuous-time channel rather than decomposing it using the continuous-time Karhunen–Loève orthogonal expansion. This permits the application of the rather simple and intuitive properties of Asymptotically Equivalent sequences of matrices to the resulting discrete time channel.