REASSIGNMENT AND MULTITAPER BASED TIME-FREQUENCY REPRESENTATIONS IN ESTIMATION OF TRANSIENT SIGNAL COMPONENTS - Kuresevic,Ida Zoe (Master’s Theses in Mathematical Sciences, 2025)
Time-frequency representations (TFR) typically suffer from resolution problems due to the uncertainty principle. This can lead to loss of information if signals are too close in time or frequency, or if they have significantly different energies. Methods addressing these issues and which can be used in tandem with the typical spectrogram or scalogram have been developed throughout the years. The reassignment method increases resolution by shifting the TFRs energy towards point of interest and the multitaper method addresses high variance by averaging over several TFRs. This thesis will look at three recently defined TFRs: the matched window reassignment (MWR), the reassigned multitaper spectrogram (ReMuS), and the reassigned multitaper scalogram (ReMuΣ). We compare these in their precision and robustness in different simulated scenarios, to find the limits at which they can still reasonably be applied. The simulations are based on dolphin echolocation data consisting of a two component signal. Of interest to us, is a short transient high frequency component preceding the main echolocation signal. Finally, we make use of the ReMuΣ on real world data of dolphin echolocation signals to describe this previously unknown energetically weak transient signal component.