Water exchange between the different compartments of a heterogeneous specimen can be characterized via diffusion magnetic resonance imaging (dMRI). Many analysis frameworks using dMRI data have been proposed to describe exchange, often using a double diffusion encoding (DDE) stimulated echo sequence. Techniques such as diffusion exchange weighted imaging (DEWI) and the filter exchange and rapid exchange models, use a specific subset of the full space DDE signal. In this work, a general representation of the DDE signal was employed with different sampling schemes (namely constant �1, diagonal and anti-diagonal) from the data reduction models to estimate exchange. A near-uniform sampling scheme was proposed and compared with the other sampling schemes. The filter exchange and rapid exchange models were also applied to estimate exchange with their own subsampling schemes. These subsampling schemes and models were compared on both simulated data and experimental data acquired with a benchtop MR scanner. In synthetic data, the diagonal and near-uniform sampling schemes performed the best due to the consistency of their estimates with the ground truth. In experimental data, the shifted diagonal and near-uniform sampling schemes outperformed the others, yielding the most consistent estimates with the full space estimation. The results suggest the feasibility of measuring exchange using a general representation of the DDE signal along with variable sampling schemes. In future studies, algorithms could be further developed for the optimization of sampling schemes, as well as incorporating additional properties, such as geometry and diffusion anisotropy, into exchange frameworks.