Time Warping in Digital Audio Effects
Time warping is an important paradigm in sound processing, which consists of composing the signal with another function of time called the warping map. This paradigm leads to different points of view in signal processing, fostering the development of new effects or the conception of new implementations of existing ones. While the introduction of time warping in continuous-time signals is in principle not problematic, time warping of discretetime signals is not self-evident. On one hand, if the signal samples were obtained by sampling a bandlimited signal, the warped signal is not necessarily bandlimited: it has a sampling theorem of its own, based on irregular sampling, unless the map is linear. On the other hand, most signals are regularly sampled so that the samples at non-integer multiples of the sampling interval are not known. While the use of interpolation can partly solve the problem it usually introduces artifacts. Moreover, in many sound applications, the computation already involves a phase vocoder. In this paper we introduce new methods and algorithms for time-warping based on warped time-frequency representations. These lead to alternative algorithms for warping for use in sound processing tools and digital audio effects and shed new light in the interaction of time warping with phase vocoders. We also outline the applications of time warping in digital audio effects.