Enhancing low-resolution, low-frame-rate videos to high-resolution, high-frame-rate quality is essential for a seamless user experience, motivating advancements in Continuous Spatial-Temporal Video Super Resolution (C-STVSR). While prior methods employ Implicit Neural Representation (INR) for continuous encoding, they often struggle to capture the complexity of video data, relying on simple coordinate concatenation and pre-trained optical flow network for motion representation. Interestingly, we find that adding position encoding, contrary to common observations, does not improve—and even degrade—performance. This issue becomes particularly pronounced when combined with pre-trained optical flow networks, which can limit the model’s flexibility. To address these issues, we propose BF-STVSR, a C-STVSR framework with two key modules tailored to better represent spatial and temporal characteristics of video: 1) B-spline Mapper for smooth temporal interpolation, and 2) Fourier Mapper for capturing dominant spatial frequencies. Our approach achieves state-of-the-art PSNR and SSIM performance, showing enhanced spatial details and natural temporal consistency. Our code will be available soon.