A New Interpretation of S-Transform Spectrum: Phase Hopping Analysis and Estimation

S-Transform (ST) is a powerful timefrequency analysis tool with several useful performances. It has been found that ST is sensitive to the sudden change of signal phase and causes a spectrum spread phenomenon, which is often regarded as a shortage. However, a new interpretation of ST spectrum is proposed: the ST can provide a better property of phase hopping detection due to the sensitivity and mono-peak response of ST spectrum. It is a beneficial method to phase hopping estimation. The mathematical relation between the phase hopping angle and the instantaneous value changes of ST spectrum is derived in an explicit representation. This work helps to make a better understanding of the ST spectrum. Besides of the formula derivation, the characteristic is also proved and confirmed by the numerical simulations.