3D Gaussian splatting-based SLAM technology enables real-time position estimation and high-quality map generation. However, it requires an iterative convergence process due to the uncertainty of Gaussian position and initialization parameters, and there is a problem that the Gaussian representation may be excessive or insufficient. In this paper, we propose a novel adaptive density method based on Fourier frequency-domain analysis to set Gaussian priors and achieve fast convergence. In addition, we present a method to independently and integratedly construct a sparse map that supports efficient tracking using the Generalized Iterative Closest Point (GICP) and a dense map that generates high-quality visual representations. This is the first SLAM system that achieves high-quality Gaussian mapping in real time by utilizing frequency-domain analysis. We achieve an average frame rate of 36 FPS on Replica and TUM RGB-D datasets, and show competitive accuracies in both position estimation and mapping.