# Time Series Anomaly Detection Using Signal Processing and Deep Learning
###### Abstract  
In this paper, we propose a two-step approach for time series anomaly detection that combines signal processing techniques with deep learning methods. In the first step, we apply a bandpass filter to the time series data to reduce noise and highlight relevant frequency components, which enhances the signals in them. In the second step, we utilize a Functional Neural Network Autoencoder for anomaly detection, leveraging its ability to capture non-linear temporal relationships in the data. By learning a compact latent representation and remapping the filtered time series, the Autoencoder effectively identifies deviations from normal patterns, allowing us to detect anomalies. Our experiments on several benchmark datasets demonstrate that bandpass filtering consistently improves the performance of deep learning methods, including the Functional Neural Network Autoencoder, by refining the input data. Our proposed approach achieves superior performance of up to 20% in detecting anomalies, particularly in a time series with intricate structures, highlighting its potential for practical applications in multiple domains. y +
Footnote †: : 2020 IEEE International Conference on Ac  
Traditional time series processing methods, such as statistical models like the ARIMA (Auto-Regressive Integrated Moving Average) [7] or signal processing techniques [8], have shown success in specific settings but often fail to adapt to complex, high-dimensional time series data. With the rise of deep learning, more sophisticated models have been developed that can automatically learn patterns in time series data without the need for extensive feature engineering. Models like Autoencoders, which is an unsupervised approach, with layers of traditional neural networks, Recurrent Neural Networks (RNNs), Transformers, and Convolutional Neural Networks (CNNs) are commonly used for time series anomaly detection [9; 10; 11]. Autoencoders have shown they can learn compact representations of normal time series data, from which they are able to remap back to the original time series and flag deviations from these learned patterns. Long Short-Term Memory (LSTM) networks, a type of RNN, are frequently used for time series analysis due to their ability to capture long-term temporal dependencies, making them particularly effective for detecting anomalies in such kind of data [12]. Recent research in deep learning has highlighted the effectiveness of more advanced architectures such as Transformers [13] and Graph Neural Networks (GNNs) [14] for time series anomaly detection. Transformers, with their self-attention mechanisms, are particularly capable of capturing global dependencies in long sequences, making them suitable for multivariate time series anomaly detection where time series feature relationships are critical. Graph Neural Networks explicitly model the relational structure between different time series features, enabling a better understanding of spatial and temporal dependencies in complex systems. As mentioned in [15; 16; 17], these deep learning approaches represent a significant leap forward in the ability to detect anomalies in real-world time series data. Another promising deep learning approach for time series analysis is the Functional Neural Network (FNN), designed to handle time series data by treating them as continuous functions rather than discrete data points [18]. This allows FNNs to capture both local and global temporal patterns, making them well suited for dealing with intricate, high-dimensional time series data. By learning non-linear relationships while preserving the temporal structure, FNNs offer a robust method for analyzing time series data. Building on this, Bi-Functional Autoencoders (BFAEs) [19] extend the FNN framework to enable dimensionality reduction using an Autoencoder architecture. The BFAE learns a compact representation of the time series, achieving efficient data compression. However, the BFAE has not been tested for anomaly detection tasks.