In order to solve the problem of identifying unknown emitters in an open electromagnetic environment， we propose an open-set identification method based on the convolutional neural network- Fourier analysis network （CNN-FAN） model. The proposed method initially introduces the network layer of Fourier analysis networks （FAN）. The Fourier series properties are utilized to effectively extract the frequency components of the signal， followed by its integration with a convolutional neural network to formulate the CNN-FAN network model. Subsequently， the Softmax layer is substituted with an open-set identification model， facilitated by the utilization of OpenMax. Finally， a joint optimization strategy combining center loss and cross-entropy loss is adopted to optimize model performance. This optimization reduces the feature distance of individual radiation sources and narrows inter-class gaps， which improves the classification performance and enables OpenMax to distinguish between known and unknown emitter categories. The proposed method is validated and subjected to experimental analysis on the open-source WiSig dataset under varying degrees of openness. Experimental results demonstrate that the proposed method attains a recognition rate of 95% at an openness level of 0.057 and an open-set recognition rate of 84% at an openness level of 0.184， thereby outperforming other open-set recognition methods. In addition， the proposed framework provides a systematic solution for open-set radio frequency fingerprint identification by jointly considering discriminative feature learning and unknown-class rejection. The CNN module captures local temporal characteristics from the input radio frequency signals， while the FAN layer further enhances the representation capability by modeling periodic and frequency-domain variations. This complementary feature extraction mechanism enables the network to obtain more robust and separable emitter-specific representations. Moreover， by incorporating OpenMax into the decision stage， the model is no longer restricted to closed-set classification and can assign samples from unseen emitters to unknown categories according to their activation distribution. The combination of feature compactness optimization and open-set probability calibration improves both known-emitter identification and unknown-emitter rejection. These results indicate that the proposed CNN-FAN-based open-set identification method has strong applicability in realistic electromagnetic environments where unknown emitters may appear during deployment.