Abstract
Synchrosqueezing transform (SST) can effectively improve time-frequency precision and resolution by squeezing time-frequency spectra via instantaneous frequencies, and it has been applied in many diverse disciplines; however, the precision of estimated instantaneous frequencies during SST is usually affected by the time-sample interval of the inputted signal; this usually leads to low-precision or inaccurate SST results and limits its further application. To obtain high-precision and high-resolution SST results with high efficiency, we propose a high-precision and high-resolution SST via time-frequency instantaneous phases (HSST); in HSST, time-frequency instantaneous phases with period-jumps removal are used for high-precision instantaneous frequencies estimation and SST. Two synthetic signal examples show that HSST can minimize the impact of the time-sample interval to achieve high-precision and high-resolution SST results with high efficiency. A real 3D seismic data application demonstrates that HSST has fantastic performance in time-frequency precision and resolution enhancement, and it can be widely used in digital signals processing and interpretation fields.
Highlights
In second-order synchrosqueezing transform (SST), instantaneous phases of the inputted signal are considered second-order functions of time and expressed by second-order Taylor expansion, and second-order partial derivatives of time-frequency spectra with respect to time and frequency are used for instantaneous frequency estimation; whereas in high-order SST, instantaneous phases are considered high-order functions of time and expressed by high-order Taylor expansion, and high-order partial derivatives of time-frequency spectra with respect to time and frequency are used for instantaneous frequency estimation
We propose a high-efficiency, high-precision, and high-resolution SST via time-frequency instantaneous phases with period-jumps removal, which is referred to as HSST; in HSST, time-frequency instantaneous phases with period-jumps removal are used for high-precision instantaneous frequencies estimation and SST
To obtain high-precision and high-resolution SST results with high-efficiency, we propose a high-precision and high-resolution SST via time-frequency instantaneous phases, which is referred to as HSST
Summary
The classical time-frequency methods, such as short-time Fourier transform (STFT) [1], wavelet transform [2,3], S transform [4,5], generalized S transform [6], modified short-time Fourier transform (MSTFT) [7,8,9], synchrosqueezing transform (SST) [10,11,12,13,14,15,16,17,18,19,20,21], and so on, have been developed into a mature set of techniques for non-linear and non-stationary digital signals analysis, processing, and interpretation Compared with these classical time-frequency methods [1,2,3,4,5,6,7,8,9], SST can effectively improve time-frequency precision and resolution by time-frequency spectra reassignment via instantaneous frequencies, and this makes SST more suitable for non-linear and nonstationary signals. Synthetic signals and real 3D seismic data examples demonstrate that HSST can be widely used for seismic signal [8,9,13,16], microseismic signal [24,25], gear vibration signal [6], gravitational-wave signal [19], and other nonstationary digital signals processing and interpretation
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