Continuous wavelet transform and higher-order spectrum: combinatory potentialities in breath sound analysis and electroencephalogram-based pain characterization

Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.

Parkinsonian Tremor Detection with Compact Convolutional Transformer from Bispectrum Representation of tri-Axial Accelerometer Signals

After the breakthroughs of Transformer networks in Natural Language Processing (NLP) tasks, they have led to exciting progress in visual tasks as well. Nonetheless, there has been a parallel growth in the number of parameters and the amount of training data, which led to the conclusion that Transformers are not suited for small datasets. This paper is the first to convey the feasibility of Compact Convolutional Transformers (CCT) for the prediction of Parkinsonian postural tremor based on the Bispectrum (BS) representation of IMU accelerometer time series. The dataset includes tri-axial accelerometer signals collected unobtrusively in-the-wild while subjects are on a phone call, and labelled by neurologists and signal processing experts. The BS is a noise-immune, higher-order representation that reflects a signal's deviation from Gaussianity and measures quadratic phase coupling. We performed comparative classification experiments using the CCT, pre-trained CNNs such as VGG-16 and ResNet-50, and the conventional Vision Transformer (ViT). Our model achieves competitive prediction accuracy and F1 score of 96% with only 1.016 M trainable parameters, compared to the ViT with 21.659 M trainable parameters, in a five-fold cross-validation scheme. Our model also outperforms pre-trained CNNs such as VGG-16 and ResNet-50. Furthermore, we show that the performance gains are maintained when training on a larger dataset of BS images. Our effort here is motivated by the hypothesis that data-efficient transformers outperform transfer learning using pre-trained CNNs, paving the way for promising deep learning architecture for small-scale, novel and noisy medical imaging datasets.Clinical relevance- Novel deep learning model for unobtrusive prediction of Parkinsonian Postural Tremor from Bispectrum image representation of tri-axial accelerometer signals collected in-the-wild.

Study of Transmission Line Boundary Protection Using a Multilayer Perceptron Neural Network with Back Propagation and Wavelet Transform

Protection schemes are usually implemented in the planning of transmission line operations. These schemes are expected to protect not only the network of transmission lines but also the entire power systems network during fault conditions. However, it is often a challenge for these schemes to differentiate accurately between various fault locations. This study analyses the deficiencies identified in existing protection schemes and investigates a different method that proposes to overcome these shortcomings. The proposed scheme operates by performing a wavelet transform on the fault-generated signal, which reduces the signal into frequency components. These components are then used as the input data for a multilayer perceptron neural network with backpropagation that can classify between different fault locations in the system. The study uses the transient signal generated during fault conditions to identify faults. The scientific research paradigm was adopted for the study. It also adopted the deduction research approach as it requires data collection via simulation using the Simscape electrical sub-program of Simulink within Matrix laboratory (MATLAB). The outcome of the study shows that the simulation correctly classifies 70.59% of the faults when tested. This implies that the majority of the faults can be detected and accurately isolated using boundary protection of transmission lines with the help of wavelet transforms and a neural network. The outcome also shows that more accurate fault identification and classification are achievable by using neural network than by the conventional system currently in use.

Introduction to redundancy rules: the continuous wavelet transform comes of age

Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)-even when it appears most appropriate for the problem at hand-is that it is 'redundant'. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, 'redundant' is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form-the CWT-is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.