Today's computing devices are mostly based on CMOS technology, built on Boolean logic, and almost exclusively represent signals electrically. The steady exponential growth of CMOS made it dominant in the past few decades, however the scale down now approaches hard limits and it encounters more and more difficulties to keep up with Moore's law. Though many believe that transistor technologies will be able to overcome these issues -- as they did so far -- it is worth to consider other technologies, even ones that were earlier outcompeted by CMOS.We investigated the usage of spin waves for computing purposes. Our approach is to directly use spin waves for wave-computing algorithms as opposed to designing novel logic gates using spin-wave signals -- which has been the more typical approach recently. We borrowed ideas from the already well established optical computing theory, but instead of using optical waves, we redesigned these concepts for spin waves. We proposed spin-wave phase shifters and lenses, and investigated different types of sources for spin-wave generation. Based on these components a spin-wave Fourier transformation and filtering device were designed, and we believe that these designs can be further expanded to holographic pattern matching devices, or other special-purpose signal-processing hardware accelerators. We verified our proof-of-principle designs using micromagnetic simulations and we are currently working on experimental demonstrations of the feasibility of our concepts.