Comprehensive Signal Processing and Anomaly Detection of Multivariate Sensor Signals Using Time - Frequency and Entropy - based Methods
Hathairat Ketmaneechairat
Digital Signal Processing and Artificial Intelligence for Automatic Learning, Vol. 5, No. 3, 2026.
DOI: https://doi.org/10.6025/dspaial/2026/5/3/135-167
Link: https://www.dline.info/dspai/fulltext/v5n3/dspaiv5n3_1.pdf
Abstract:
Low cost Micro Electromechanical Systems (MEMS) sensors are widely deployed in embedded systems, the
Internet of Things (IoT), and cyber physical environments; however, their raw output under nominally static
conditions may exhibit substantial temporal, spectral, distributional, and statistical complexity that cannot
be captured by a single analytical representation. This study proposes and applies an integrated multidomain
signal processing and unsupervised anomaly detection framework for the comprehensive characterization of
multivariate static MEMS accelerometer data. The framework combines time domain statistics, Fast Fourier
Transform (FFT) and Welch power spectral density (PSD) analysis, short time Fourier transform spectrograms,
wavelet domain energy decomposition, autocorrelation and rolling root mean square (RMS) analysis, Pearson
inter channel correlation, signal to noise ratio (SNR) estimation, Shannon and spectral entropy measures,
rolling statistical change point detection, and two complementary unsupervised anomaly detection methods
Isolation Forest and PCA reconstruction based detection. The framework is applied to a four channel dataset
acquired from a stationary MPU-6050 accelerometer, comprising three raw acceleration axes and a derived
percentage error channel, containing approximately 37,459 observations. The results reveal pronounced
heterogeneity among the sensor channels: Sensors 1, 2, and 4 exhibit strongly non Gaussian, heavy tailed
amplitude distributions with extreme skewness and excess kurtosis, whereas Sensor 3 displays substantially
greater amplitude variability, strong temporal persistence, and concentrated spectral organization. Frequency
domain analysis identifies a distinctive approximately 21 sample periodic component in Sensor 2, while time
frequency and wavelet analyses expose localized transient events not captured by global spectral summaries.
Dual entropy analysis demonstrates that amplitude domain and frequency domain complexity are distinct
and independently informative properties. Change point detection identifies two statistical regime transitions,
and both Isolation Forest and PCA reconstruction consistently identify 24 anomalous windows (anomaly
rate Hâ€ 1.028%) in the absence of predefined labels. The integrated findings demonstrate that no single
analytical domain is sufficient to characterize static MEMS sensor behavior, and that a multidomain framework
is necessary to distinguish persistent nominal structure, transient anomalous deviations, and sustained
statistical regime changes. The proposed framework provides a structured, reproducible, and label-free
analytical foundation for sensor monitoring and anomaly detection in resource constrained and IoT-enabled
systems.