synchrosqueezing

Synchrosqueezing is a post-processing technique used in time-frequency analysis to produce a sharpened representation of a signal’s instantaneous frequency content. It aims to concentrate the energy of a time-frequency representation along smooth curves that correspond to the instantaneous frequencies of the signal’s components, improving interpretability and enabling more accurate component extraction.

The method starts from a standard time-frequency representation, such as the short-time Fourier transform or the continuous wavelet transform. It then estimates the instantaneous frequency at each point via the local phase information, often using the derivative of the transform with respect to time. Energy at a given time and frequency is reassigned to a nearby frequency equal to the estimated instantaneous frequency. The result is a “squeezed” representation that has reduced smearing and better alignment with actual frequency trajectories.

Synchrosqueezing is particularly useful for multi-component signals with slowly varying amplitudes and frequencies, as it enhances ridge localization and facilitates the separation and reconstruction of individual components. Variants include those based on different base transforms and higher-order formulations designed to improve frequency estimation and robustness to noise.

Applications span various fields, including biomedical signal processing (such as ECG and EEG), acoustics and speech, vibration analysis, seismology, and other areas where non-stationary signals are analyzed. Compared with traditional time-frequency methods, synchrosqueezing offers sharper representations, while relying on well-established mathematical foundations in time-frequency analysis and reassignment techniques.