Kernel techniques for generalized audio crossfades

• Main Authors: William A. Sethares, James A. Bucklew
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2015-12-01
• Series: Cogent Mathematics
• Subjects: audio crossfade; morphing; kernel techniques; Poisson process; interpolation
• Online Access: http://dx.doi.org/10.1080/23311835.2015.1102116

This paper explores a variety of density and kernel-based techniques that can smoothly connect (crossfade or “morph” between) two functions. When the functions represent audio spectra, this provides a concrete way of adjusting the partials of a sound while smoothly interpolating between existing sounds. The approach can be applied to both interpolation crossfades (where the crossfade connects two different sounds over a specified duration) and to repetitive crossfades (where a series of sounds are generated, each containing progressively more features of one sound and fewer of the other). The interpolation surface can be thought of as the two dimensions (time and frequency) of a spectrogram, and the kernels can be chosen so as to constrain the surface in a number of desirable ways. When successful, the timbre of the sounds is changed dynamically in a plausible way. A series of sound examples demonstrate the strengths and weaknesses of the approach.