Current state of nonlinear-type time–frequency analysis and applications to high-frequency biomedical signals

Ultra-Resolution Spectral Correction Based on Adaptive Linear Neuron for Biomedical Signal Processing

“…After establishing the AR model, data extrapolation can be made. Beside the available data, additional samples can be predicted using Equation (1). The flow chart of the proposed method is displayed in Figure 1B.…”

“…Sinusoidal waves (SWs) are often presented in engineering dynamic measurements. They also appear in biomedical signals (1)(2)(3), such as electrocardiogram (ECG), electroencephalogram (EEG) and electromyography (EMG). The power line interference (4-6) is among the major types of interferences in these biomedical signals and it should be removed using hardware or software based techniques (7)(8)(9).…”

Oscillatory Biomedical Signals: Frontiers in Mathematical Models and Statistical Analysis

“…Combining time-frequency analysis (TFA) with statistical analysis, the lack of which in the previous work "presents an opportunity for much future research," is illustrated in Figure 2 (applied to PPG, fetal ECG, and fetal heart rate variability) of Wu [2] who describes several recent advances in TFA for highfrequency biomedical signals. There are several challenges common to different biomedical signal processing problems.…”

“…. , θ N from p(•) dm and using the sample averageμ 2 and ζ q is the qth quantile of the standard normal distribution. This follows from the classical central limit theorem and is very useful for determining N to ensureμ to be within some prescribed tolerance limit ϵ of μ: N −1/2σ N ζ 1−α/2 # ϵ and has inspired Lai to develop, with his current Ph.D. students Huanzhong Xu, Michael Hongyu Zhu, and former Ph.D. student Hock Peng Chan, the following novel MCMC algorithm which is asymptotically equivalent to the oracle procedure that assumes known target density p and which they call MCMC with sequential state substitutions (MCMC-SS).…”

Wave-shape oscillatory model for nonstationary periodic time series analysis

“…However, these methods are inherently limited when the time series' period and amplitude of oscillation, not to mention the wave-shape, are non-constant. Modern time-frequency analysis tools [27], particularly nonlineartype time-frequency analysis tools [58] like the synchrosqueezing transform (SST), have been considered for non-seasonal signals [12]; however, as we will carefully discuss in the supplementary material, both the model behind the original SST and its generalization [34] fail when modulations in frequency, amplitude, or wave-shape do not occur gradually (a phenomenon commonly seen when the underlying human system assumes pathophysiological status). Since well-behaved human systems are rarely of clinical interest, this challenge necessitates a different model for analyzing oscillatory physiological time series and, in particular, a tool for extracting the dynamics encoded by the time-varying morphology of their cycles.…”