The scaled reassigned spectrogram adapted for detection and localisation of transient signals

The reassigned spectrogram can be used to improve the readability of a time-frequency representation of a non-stationary and multi-component signal. However for transient signals the reassignment needs to be adapted in order to achieve good localisation of the signal components. One approach is to scale the reassignment. This paper shows that by adapting the shape of the time window used with the spectrogram and by scaling the reassignment, perfect localisation can be achieved for a transient signal component. It is also shown that without matching the shape of the window, perfect localisation is not achieved. This is used to both identify the time-frequency centres of components in a multi-component signal, and to detect the shapes of the signal components. The scaled reassigned spectrogram with the matching shape window is shown to be able to resolve close components and works well for multi-components signals with noise. An echolocation signal from a beluga whale (Delphinapterus leucas) provides an example of how the method performs on a measured signal.