ESPRIT in Gabor frames
Authors: Sirdey A., Derrien O., Kronland-Martinet R., Aramaki M.
Publication Date: March 2012
Journal: Proceedings of the AES 45th International Conference (pp. 305-313, Helsinki, Finland, 1-4 March 2012)
Tags: Gabor Frames, Timbre
This articles tackles the estimation of mode parameters in recorded sounds of resonant objects. High resolution methods such as the ESPRIT method have already proved to be of great use for this sort of purpose. However, these methods being model-sensitive, their application to real-life audio signals can lead to results that are not satisfactory enough for a consistent re-synthesis. This is especially the case when the computational cost makes it impossible to analyse the signal in totality, or when the signal presents a high number of components. Significant improvements have already been achieved by decomposing the signal into several sub-band filtered versions, and by applying the ESPRIT algorithm on each of the resulting signals. It is shown in this article that the ESPRIT algorithm can be efficiently applied on time-frequency representations of the signal obtained using Gabor frames. Numerical tests that highlight the advantages of such an approach are also detailed. In addition to the advantages offered by the sub-band approach, the solid Gabor frame formalism combined with the ESPRIT method allows a flexible and sharp analysis on selected regions of the time-frequency plane, and leads to re-synthesis which are perceptually very close to the original sounds.
The original sound results from the hit of a metal bowl:
Details on the re-synthesized sounds:
Sound 1: Re-synthesis with the full-band ESPRIT algorithm, arbitrarily setting the negative dampings to 1
Sound 2: Re-synthesis with the full-band ESPRIT algorithm, after discarding the components with a negative damping
Sound 3: Re-synthesis with ESPRIT applied in a Gabor frame
Sound 4: Re-synthesis with ESPRIT applied in a Gabor frame, after discarding the irrelevant components