FFT-Based Anomaly Detectors: Cutoff Frequency Adjustment and SMA-Based Approach
DOI:
https://doi.org/10.5753/jidm.2026.5732Keywords:
Anomaly Detection, Time Series Analysis, FFT, High-Pass Filtering, FFT-Based DetectorsAbstract
This article presents a method for anomaly detection in time series based on the Fast Fourier Transform (FFT) using high-pass filtering. In addition to five existing strategies for determining the cutoff frequency (TF, AF, CAF, BSF, CBSF), a novel approach called SMAF is introduced. SMAF combines spectral analysis with adaptive smoothing using the Simple Moving Average, enabling the detection of high-frequency anomalies without requiring the inverse transform. The experiments employ the Yahoo Webscope dataset and the Numenta Anomaly Benchmark (NAB), providing a comprehensive evaluation. FFT-based approaches are compared to traditional statistical techniques (FBIAD and ARIMA) and machine learning methods (LSTM, ELM, and SVM). The results show that FFT-based methods outperform both statistical and machine learning techniques in terms of F1 score, precision, accuracy, and execution time. Among them, SMAF achieves the highest precision and the lowest execution time, reinforcing the potential of FFT-based filtering for efficient and accurate anomaly detection in time series.
Downloads
References
Alghamdi, H. A., Adham, M. A., and Bass, R. B. (2024). Analyzing frequency event detection algorithm performance using different denoising methods. In 2024 IEEE Conference on Technologies for Sustainability (SusTech), pages 294–301. IEEE.
Bhattacharya, C., De, S., Mukhopadhyay, A., Sen, S., and Ray, A. (2020). Detection and classification of lean blow-out and thermoacoustic instability in turbulent combustors. Applied Thermal Engineering, 180. DOI: 10.1016/j.applthermaleng.2020.115808.
Bürger, F. and Pauli, J. (2013). Unsupervised segmentation of anomalies in sequential data, images and volumetric data using multiscale fourier phase-only analysis. In LNCS, volume 7944, pages 44 – 53. DOI: 10.1007/978-3-642-38886-65.
Collins Jackson, A. and Lacey, S. (2020). The discrete Fourier transformation for seasonality and anomaly detection of an
application to rare data. Data Technologies and Applications, 54(2):121 – 132. DOI: 10.1108/DTA-12-2019-0243.
Erkuş, E. C. and Purutçuoğlu, V. (2021). Outlier detection and quasi-periodicity optimization algorithm: Frequency domain based outlier detection (FOD). European Journal of Operational Research, 291(2):560 – 574. DOI: 10.1016/j.ejor.2020.01.014.
Han, J., Pei, J., and Tong, H. (2022). Data Mining: Concepts and Techniques. Morgan Kaufmann, Cambridge, MA, 4th edition edition.
Herrera, M., Proselkov, Y., Perez-Hernandez, M., and Parlikad, A. K. (2021). Mining Graph-Fourier Transform Time Series for Anomaly Detection of Internet Traffic at Core and Metro Networks. IEEE Access, 9:8997 – 9011. DOI: 10.1109/AC- CESS.2021.3050014.
Jiang, J.-R., Kao, J.-B., and Li, Y.-L. (2021). Semi-supervised time series anomaly detection based on statistics and deep learning. Applied Sciences (Switzerland), 11(15). DOI: 10.3390/app11156698.
Killick, R. and Eckley, I. A. (2014). Changepoint: An R package for changepoint analysis. Journal of Statistical Software, 58(3):1 – 19. DOI: 10.18637/jss.v058.i03.
Lima, J., Salles, R., Porto, F., Coutinho, R., Alpis, P., Escobar, L., Pacitti, E., and Ogasawara, E. (2022). Forward and Backward Inertial Anomaly Detector: A Novel Time Series Event Detection Method. In Proceedings of the IJCNN, volume 2022-July, pages 1–8. DOI: 10.1109/IJCNN55064.2022.9892088.
Lindstrom, M. R., Jung, H., and Larocque, D. (2020). Functional kernel density estimation: Point and fourier approaches to time series anomaly detection. Entropy, 22(12):1 – 15. DOI: 10.3390/e22121363.
Loyarte, M. G. and Menenti, M. (2008). Impact of rainfall anomalies on Fourier parameters of NDVI time series of northwestern Argentina. International Journal of Remote Sensing, 29(4):1125 – 1152. DOI: 10.1080/01431160701355223.
Lykou, R., Tsaklidis, G., and Papadimitriou, E. (2020). Change point analysis on the Corinth Gulf (Greece) seismicity. Physica A: Statistical Mechanics and its Applications, 541. DOI: 10.1016/j.physa.2019.123630.
Olteanu, M., Rossi, F., and Yger, F. (2023). Meta-survey on outlier and anomaly detection. Neurocomputing, 555. DOI: 10.1016/j.neucom.2023.126634.
Oppenheim, A. V., Willsky, A. S., and Nawab, S. H. (1997). Signals & Systems. Prentice Hall. Rong, K. and Bailis, P. (2017). Asap: prioritizing attention via time series smoothing. arXiv preprint arXiv:1703.00983.
Silva, E. P., Balbi, H., Pacitti, E., Porto, F., dos Santos, J. A., and Ogasawara, E. S. (2024). Cutoff frequency adjustment for fft-based anomaly detectors. In SBBD 2024-Simpósio Brasileiro de Banco de Dados, pages 1–5.
Ye, Y., He, Q., Zhang, P., Xiao, J., and Li, Z. (2023). Multivariate Time Series Anomaly Detection with Fourier Time Series Transformer. In 2023 IEEE 12th CloudNet 2023, pages 381 – 388. DOI: 10.1109/CloudNet59005.2023.10490086.
Yu, Y., Zhu, Y., Li, S., and Wan, D. (2014). Time series outlier detection based on sliding window prediction. Mathematical Problems in Engineering, 2014. DOI: 10.1155/2014/879736.
Zhao, H., Lu, B., Yu, L., Zhao, S., Zeng, L., Zhang, Z., and You, P. (2018). A fourier series-based anomaly extraction approach to access network traffic in power telecommunications. In 2017 ICCSEC, pages 550 – 553. DOI: 10.1109/ICC- SEC.2017.8446807.
Zhou, L., Guo, W., Cao, J., Zhang, X., and Wang, Y. (2023). Wavelet-SVDD: Anomaly Detection and Segmentation with Frequency Domain Attention. In LNAI, volume 14177, pages 230 – 243. DOI: 10.1007/978-3-031-46664-916.
