The bilateral filter is an edge-aware image filter. While it has a variety of applications, its naive implementation is quadratic in nature, hindering the ability to efficiently process multi-megapixel images. If performance is needed, like in a real-time setting, an approximation is necessary. Current literature on Fourier series-based approximations does not explore the capabilities of graphics processing units (GPUs) as viable platforms for this computational problem. This paper proposes an approach for implementing such filtering on a GPU by conducting a series of separable convolutions, and also investigates the use of different range kernels. Our adaption of the bilateral filter is found to be more two times faster than readily available solutions, with frame times showing that real-time performance is possible for large spatial kernel sizes and image resolutions.