The subband identification method is a relatively new approach that can be considered as a generalization of the time domain and frequency domain methods since the identification is carried out in the time-frequency domain. The main advantage of this method is its great numerical efficiency.
Obviously, the subband technique can also be used to approximate a linear (possibly time variant) system in the time-frequency domain. In this project we propose to exploit modern time-frequency analysis techniques to t he analysis and further development of the subband technique. We will start by considering different mathematical frameworks were we could better interpret and analyze the problem.
We will exploit the connection between Gabor (or frame) multipliers and sub band models, and we will exploit the fact that the coefficients of the subband model of a system can be interpreted as the coefficients of a system frame decomposition.
We expect that these approaches will not only provide results readily applicable to the subband system identification and approximation techniques, but will also provide the theoretical foundation for the rest of the project. After this, we will use two concrete ideas from time-frequency analysis of signals, to look for improvements of the subband system identification method.
The first idea is to use time-variant adaptive filterbanks, and to adapt them to maximize some sparsity criterion on the subband model of the system. The second idea aims to simplify the complexity of the identification algorithm by adapting the filterbanks to maximize the some sparsity criterion on the systems output signal, and then run the algorithm only on the significant parts of this signal.
Finally, we intend to use our results, for two applications (a) shift invariant sparse coding and convolutive blind source separation of audio signals (b) real time implementation of a high quality sound synthesis method called digital waveguide synthesis.
Call for proposal
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