As sharing digital media is getting more prominent, there has been a rise in the development of techniques for protecting digital media against misuse. However, the amount of such techniques has been less prominent for printed goods. The data hiding method presented in this paper is suited for the print domain. The method uses the Discrete Fourier Transform to embed data into images and Gray Component Replacement to maintain high image quality by masking embedding artifacts. This research examines whether the method's performance can be optimized using low-frequency ranges for embedding. The aim is to evaluate the usage of low-frequency ranges in order to achieve higher robustness. Different frequency ranges are tested to determine how they affect image quality and detection rates. Tests are conducted in the digital domain. The results show that the method can maintain image quality regardless of the frequency range, and that low-frequency ranges lead to more consistent detection rates. Future research will be done on images in the print domain.