Cross-resolution face recognition has become a challenging problem for modern deep face recognition systems. It aims at matching a low-resolution probe image with high-resolution gallery images registered in a database. Existing methods mainly leverage prior information from high-resolution images by either reconstructing facial details with super-resolution techniques or learning a unified feature space. To address this challenge, this paper proposes a new approach that enforces the network to focus on the discriminative information stored in the low-frequency components of a low-resolution image. A cross-resolution knowledge distillation paradigm is first employed as the learning framework. Then, an identity-preserving network, WaveResNet, and a wavelet similarity loss are designed to capture low-frequency details and boost performance. Finally, an image degradation model is conceived to simulate more realistic low-resolution training data. Consequently, extensive experimental results show that the proposed method consistently outperforms the baseline model and other state-of-the-art methods across a variety of image resolutions.