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