Matched Gaussian Multitaper Spectrogram

A novel multitaper spectrogram estimator for Gaussian func- tions is proposed. The multitapers are the Hermite functions and a fixed number of few multitapers are used in the estimate. The weighting factors of the different spectrogram functions are optimized to give the approximative Wigner distribution for the Gaussian function. The performance of the estimator is investigated in terms of resolution and cross-term reduc- tion in the time-frequency domain. Additionally, a simula- tion example shows the robustness against white noise distur- bances. The performance of the new estimator is compared to the Wigner distribution, the usual spectrogram as well as the Choi-Williams and the Born-Jordan distributions

Automatic time-frequency analysis of echolocation signals using the matched Gaussian multitaper spectrogram

High-resolution time-frequency (TF) images of multi-component signals are of great interest for visualization, feature extraction and estimation. The matched Gaussian multitaper spectrogram has been proposed to optimally resolve multi-component transient functions of Gaussian shape. Hermite functions are used as multitapers and the weights of the different spectrogram functions are optimized. For a fixed number of multitapers, the optimization gives the approximate Wigner distribution of the Gaussian shaped function. Increasing the number of multitapers gives a better approximation, i.e. a better resolution, but the cross-terms also become more prominent for close TF components. In this submission, we evaluate a number of different concentration measures to automatically estimate the number of multitapers resulting in the optimal spectrogram for TF images of dolphin echolocation signals. The measures are evaluated for different multi-component signals and noise levels and a suggestion of an automatic procedure for optimal TF analysis is given. The results are compared to other well known TF estimation algorithms and examples of real data measurements of echolocation signals from a beluga whale (Delphinapterus leucas) are presented