Recent works with an implicit neural function shed light on representing images in arbitrary resolution. However, a standalone multi-layer perceptron shows limited performance in learning high-frequency components. In this paper, we propose a Local Texture Estimator (LTE), a dominant-frequency estimator for natural images, enabling an implicit function to capture fine details while reconstructing images in a continuous manner. When jointly trained with a deep super-resolution (SR) architecture, LTE is capable of characterizing image textures in 2D Fourier space. We show that an LTE-based neural function achieves favorable performance against existing deep SR methods within an arbitrary-scale factor. Furthermore, we demonstrate that our implementation takes the shortest running time compared to previous works.