Instantaneous frequency estimation by the reassigned Stockwell spectrogram

The Stockwell transform, a mix of the short-time Fourier transform and the wavelet transform, has been widely used in practice in the last decade due to its easily interpretable and multi-resolution time-frequency characteristics. In this paper, we introduce the reassigned Stockwell spectrogram by re-mapping the surface of the spectrogram of the Stock-well transform with the aim to improve its readability. We first define and mathematically validate the channelized instantaneous frequency (CIF) and the local group delay (LGD) for the Stockwell transform. At any given point in the time-frequency domain, the associated CIF and LGD provide a re-estimation of the time arrival and instantaneous frequency of the signal component observed at that point. Thus, the reassigned Stockwell spectrogram has signal energy highly concentrated at the instantaneous frequency/group delay curves and greatly increases the resolution and readability of the time-frequency structure of the underlying signal. The instantaneous frequencies of signal components can then be extracted by detecting the local energy peaks in the reassigned Stockwell spectrogram. The difference between the reassigned and conventional Stockwell spectrograms is illustrated using both synthetic and real signals.