In the field of intrusion detection, existing deep learning algorithms have limited capability to effectively represent network data features, making it challenging to model the complex mapping relationship between network data and attack behavior. This limitation, in turn, impacts the detection accuracy of intrusion detection systems. To address this issue and further enhance detection accuracy, this paper proposes an algorithm called the Fourier Neural Network (FNN). The core of FNN consists of a Deep Fourier Neural Network Block (DFNNB), which is composed of a Hadamard Neural Network (HNN) and a Fourier Neural Network Layer (FNNL). In a DFNNB, the HNN is responsible for sampling the network intrusion data samples in different time domain spaces. The FNNL, on the other hand, performs a Fourier transform on the samples outputted by the HNN and maps them to the frequency domain space, followed by a filtering process. Finally, the data processed by filtering are transformed back to the time domain space for subsequent feature extraction work by the DFNNB. Additionally, to enhance the algorithm’s detection accuracy and filter out noise signals, this paper also introduces a High-energy Filtering Process (HFP), which eliminates noise signals from the data signal and reduces interference on the final detection result. Due to the ability of FNN to process network data in both the time domain space and the frequency domain space, it possesses a stronger capability in expressing data features. Finally, this paper conducts performance evaluations on the KDD Cup99, NSL-KDD, UNSW-NB15, and CICIDS2017 datasets. The results demonstrate that the proposed FNN-based IDS model achieves higher detection rates, lower false alarm rates, and better detection performance than classical deep learning and machine learning methods.