Plots show results from lattice simulations with lattice points (blue) and with points (red). Solid lines show the GW spectrum obtained from simulations which were performed as in this Letter but with more accurate approximations for the spatial derivatives as explained in the text. One can see that both simulations carried out with different resolutions agree very well, which indicates that the resolutions of both simulations are sufficient up to . Dashed lines show the GW spectrum generated after , in order to distinguish the GW signal produced by oscillons from the foreground produced earlier from tachyonic oscillations. We can see that in both simulations a peak in the GW spectrum forms at a characteristic frequency corresponding to the physical mass scale (denoted by the solid black line). However, this growth stops at some point, and the peak gets redshifted (cf., lower right plot). Although GWs continue to be produced at the characteristic frequency, the production efficiency decreases over time, and the peak remains too low to be clearly visible, when compared to the foreground GW spectrum.