Linear and synchrosqueezed time–frequency representations revisited: Overview, standards of use, resolution, reconstruction, concentration, and algorithms

• DOI: 10.1016/j.dsp.2015.03.004
• Publication Date: 2015-04-05T23:56:56Z
• Authors: Dmytro Iatsenko; Peter V.E. McClin...; Aneta Stefanovska
• Keywords: SIGNAL (programming language)

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review these TFRs, summarizing all practically relevant aspects use, reconsidering some conventions introducing new concepts procedures to advance applicability value. Furthermore, detailed numerical theoretical study three specific questions is provided, application methods, namely: effects window/wavelet parameters on resultant TFR; relative performance different approaches for estimating components in signal from its advantages/drawbacks synchrosqueezing. In particular, show that higher concentration transforms does not seem imply better resolution properties, so SWFT SWT do appear any significant advantages over original WFT WT apart more visually appealing pictures. The algorithms Matlab codes used this work, e.g. those calculating (S)WFT (S)WT, are freely available download.