Ludwig-Maximilians-Universität München / Mathematisches Institut der Universität München
In this talk I will introduce a new randomized approach for discretizing continuous time-frequency transforms. The idea is to randomly sample points from the time-frequency space, replacing the continuous synthesis, which is based on integration, with a Monte Carlo approximation. Since the error in the Monte Carlo approximation does not depend on the dimension of the domain of integration, the new approach allows us to consider high dimensional time-frequency spaces. Hence, we can take a standard continuous time-frequency transform, like the short time Fourier transform, and add to its 2D time-frequency plane additional feature dimensions that control other aspects of the window, e.g., the support size of the window. This enriches the expressivity of the transform without increasing computational complexity. As an example application, I will show how to derive a high dimensional phase vocoder with the complexity of a low dimensional method.