Laplacian Directed Audio Morphing
Abstract
Inspired by a formal analogy between the two dimensional version of Laplace's partial differential equation and the two dimensions (time and frequency) of a spectrogram, this paper explores a variety of density and kernelbased techniques that can smoothly connect (morph between) two functions. When the functions represent audio spectra, this presents a solution to the problem of audio morphing, providing a concrete way of adjusting the overtones of a sound while smoothly interpolating between existing sounds. The approach can be applied to both interpolation morphing (where the morph connects two different sounds over some specified duration) and to repetitive morphing (where a series of sounds are generated, each containing progressively more features of one sound and fewer of the other). 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. * Both sethares@ece.wisc.edu and bucklew@engr.wisc.edu are with the
Key takeaways
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AI
- This paper establishes a novel audio morphing technique based on Laplace's partial differential equation.
- Morphing can be categorized into interpolation and repetitive types, each with distinct applications.
- The proposed method avoids feature selection errors by using density and kernel functions directly.
- Sound examples illustrate the effectiveness and limitations of the morphing approach.
- The ridge theorem outlines conditions for connecting spectral peaks across morphing transitions.
References (19)
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- Sound examples accompanying Laplacian Directed Audio Morphing may be found at http://eceserv0.ece.wisc.edu/ ˜sethares/ papers/audioMorph.html