Description

This Master Prompt develops a comprehensive framework for examining signal behaviour across temporal, spectral, time–frequency and multiscale representations. It covers time-domain statistics, correlation, Fourier analysis, power spectral density, envelope analysis, short-time Fourier transforms, continuous and discrete wavelet transforms, synchrosqueezing and adaptive signal decomposition. Drawing on the supplied studies of weak periodic fault features, pump-turbine pressure pulsations, tool-wear monitoring, manufacturing stability, EEG frequency-band fusion and ultrasound representations, it addresses transient events, harmonics, nonstationarity and evolving frequency components. Particular attention is given to sampling conditions, window selection, spectral leakage, resolution trade-offs, boundary effects, mode mixing and parameter sensitivity. The framework distinguishes descriptive representations from validated physical explanations and requires analytical choices to preserve amplitude, frequency, temporal context and uncertainty. It supports reproducible comparisons among methods while connecting extracted patterns with independently verified system behaviour.