Quasi Monte Carlo Time-Frequency Analysis
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We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such methods using a quasi-Monte Carlo (QMC) approach. The QMC method speeds up computations, since the number of samples required for a certain accuracy is log-linear in the resolution of the signal space, and depends only weakly on the resolution of the time-frequency space, which is typically higher. We focus on signal processing based on the localizing time-frequency transform (LTFT). In the LTFT, the time-frequency plane is enhanced by adding a third axis. This higher dimensional time-frequency space improves the quality of some time-frequency signal processing tasks, like phase vocoder (an audio signal processing effect). Since the computational complexity of the QMC is log-linear in the resolution of the signal space, this higher dimensional time-frequency space does not degrade the computation complexity of the QMC method. This is in contrast to more standard grid based discretization methods, that increase exponentially in the dimension of the time-frequency space. The QMC method is also more efficient than standard Monte Carlo methods, since the deterministic QMC sample points are optimally spread in the time-frequency space, while random samples are not.
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