Deep neural networks (DNNs) have become valuable assets due to their success in various tasks, but their high training costs also make them targets for model theft. Fingerprinting techniques are commonly used to verify model ownership, but existing methods either require training many additional models, leading to increased costs, or rely on GANs to generate fingerprints near decision boundaries, which may compromise image quality. To address these challenges, we propose a GAN-based fingerprint generation method that applies frequency-domain perturbations to normal samples, effectively creating fingerprints. This approach not only resists intellectual property (IP) threats, but also improves fingerprint acquisition efficiency while maintaining high imperceptibility. Extensive experiments demonstrate that our method achieves a state-of-the-art (SOTA) AUC of 0.98 on the Tiny-ImageNet dataset under IP removal attacks, outperforming existing methods by 8%, and consistently achieves the best ABP for three types of IP detection and erasure attacks on the GTSRB dataset. Our source code is available at https://github.com/wason981/Frequency-Fingerprinting.