Résumé
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.