The multitaper reassigned spectrogram for oscillating transients with Gaussian envelopes

Joint time-frequency representations are important tools when estimating the instantaneous frequency. The widely used spectrogram is known to have poor energy localisation, which the reassignment method improves. However, the reassignment method is sensitive to noise. In this paper we present a multitaper reassigned spectrogram (MTRS) that is robust to noise and tailored to short duration transient signals. The MTRS is designed for oscillating transients with Gaussian envelopes and uses the Hermite functions as windows. The novel reassignment coordinates needed for the MTRS are derived in this paper. The MTRS localises energy at the instantaneous frequencies of transients, while white Gaussian noise is made flatter by the use of multiple windows. It is shown that the MTRS is more noise robust compared to reassignment with just one window, and that it improves on the energy localisation of the spectrogram. Thus, our MTRS is sparse, easy to interpret, and well suited for instantaneous frequency estimation, even for signals with overlapping transients and low signal-to-noise ratios.