Frugal Wavelet Transform for detecting faults in non-stationary signals (with Matlab codes)

According to the literature, one of the most notable weaknesses of the Wavelet Transform (WT) is its dependence on the selection of the wavelet function, resulting in different wavelet functions yielding varying results. To overcome this weakness, this paper introduces a new transform called the FrugWT (FrugWT). The Frugal Wavelet Transform, a type of discrete wavelet transform, emphasizes the preservation and approximation of detail signals, especially when the detection of local abrupt changes in the signal is apparently not possible. This study demonstrates that the FrugWT mitigates the influence of wavelet function selection on fault detection and exhibits resilience to acceptable noise levels. The FrugWT outperforms both the WT and signal derivative methods. Its effectiveness is demonstrated in detecting subtle faults within arrhythmic heartbeats (ECG) and abnormal brainwaves (EEG) signals. Matlab code is available in the appendix.