Among various developments in the field of computer vision, single image super-resolution of images is one of the most essential tasks. However, compared to the integer magnification model for super-resolution, research on arbitrary magnification has been overlooked. In addition, the importance of single image super-resolution at arbitrary magnification is emphasized for tasks such as object recognition and satellite image magnification. In this study, we propose a model that performs arbitrary magnification while retaining the advantages of integer magnification. The proposed model extends the integer magnification image to the target magnification in the discrete cosine transform (DCT) spectral domain. The broadening of the DCT spectral domain results in a lack of high-frequency components. To solve this problem, we propose a high-frequency attention network for arbitrary magnification so that high-frequency information can be restored. In addition, only high-frequency components are extracted from the image with a mask generated by a hyperparameter in the DCT domain. Therefore, the high-frequency components that have a substantial impact on image quality are recovered by this procedure. The proposed framework achieves the performance of an integer magnification and correctly retrieves the high-frequency components lost between the arbitrary magnifications. We experimentally validated our model’s superiority over state-of-the-art models.