This article presents a time series anomaly detection method based on the Fast Fourier Transform (FFT) using a high-pass filter. The proposed method aims to remove low-frequency components, such as trends and seasonality, which represent the normal behavior of the series, while preserving high-frequency components associated with anomalies. The major challenge in constructing this method lies in determining the high-pass filter's cutoff frequency without prior knowledge of the intrinsic nature of the series. In addition to the traditional approach, four new distinct approaches were explored to determine the high-pass filter's cutoff frequency, making the method adaptable to various datasets. Experimental results show the effectiveness of the method in anomaly detection using high-pass FFT filters that have a cutoff frequency adjusted by change points, outperforming traditional techniques such as statistical and machine learning methods in terms of F1 score, precision, accuracy, and execution time.