Approximations for Online Computation of Redressed Frequency Warped Vocoders

Gianpaolo Evangelista
DAFx-2014 - Erlangen
In recent work, the construction of non-uniform generalized Gabor frames for the time-frequency analysis of signals has been introduced. In particular, while preserving perfect reconstruction, these frames allow for tilings of the time-frequency plane with arbitrary allocation of partially overlapping frequency bands or time intervals. In a recent paper, the author demonstrated that the construction of such frames can be entirely based on warping operators, which are specified by the required frequency or time warping maps, which, in turn, interpolate the desired frequency or time intervals edges. However, while the online computation of Gabor expansions on non-uniform time intervals presents little or no problem, the computation of Gabor expansions on non-uniform frequency bands requires knowledge of the Fourier transform of the entire signal, which precludes online computation. In this paper we introduce approximations and ideas for the design of nearly perfect reconstruction analysis and synthesis atoms, which allow for the online computation of time-frequency representations on non-uniform frequency bands.