An upper bound for the frequency dependent energy of the 2-dimensional system function

In Magnetic Particle Imaging, the behavior of the system matrix energy in dependence of the frequency components has been investigated and relations have been observed. Due to the lack of a closed-form expression for the 2-or 3-dimensional system function, no expression for the energy has been obtained thus far. In this work, we use the recently found expression for the 2-dimensional system function to derive an upper bound for the energy of the 2-dimensional system function as a function of the frequency components. The comparison of the upper bound with the energy of a simulated system matrix confirms the results.