Frequency domain volume rendering (FVR) is a volume rendering technique with lower computational complexity as compared to other volume rendering techniques. In this paper the original FVR algorithm is significantly accelerated by performing the rendering stage computations on the GPU. The overall hardware-accelerated pipeline is discussed and the changes according to previous work are pointed out. The three-dimensional transformation into frequency domain is done in a pre-processing step. In the rendering step first the projection slice is extracted. The pre-computed frequency response of the three-dimensional data is stored as a 3D texture. Four different interpolation schemes for resampling the slice out of a 3D texture are presented. The resampled slice is then transformed back into the spatial domain using the inverse Fast Fourier or Fast Hartley Transform. The rendering step is implemented as a set of shader programs and is executed on running on programmable graphics hardware achieving highly interactive framerates.