Interpolating Break-Point Sets To Obtain Sound Transformations Distinct From a Cross-Fade

Introduction The genesis of this article can be traced to the following question: given two short time-domain segments of audio, are there time-domain methods for transforming one into the other distinct from a cross-fade? Methods of morphing in the frequency domain have been explored (for instance, see Depalle et al 1993, Slaney et al 1996). Yet, the author has fo und a rewarding set of transformations by considering the subset of time amplitude curves modeled via break-point sets. This is the domain of break-point interpolation synthesis (Bernstein and Cooper 1976, Mitsuhashi 1982a). Algorithms for the interpolation of break-point sets are investigated herein as pertaining to sound transformation. Since break-point sets may be useful wherever two or more parameters are mapped against each other, the transformations can have applicability to situations other than time amplitude curves. For instance, a function constructed from a break-point set could determine a center frequency versus amplitude map for a filterbank at one instant. As break-point sets are interpolated over time, the filter will change dynamically. Alternatively, break-point sets could determine surfaces, using NURBS or otherwise. These surfaces are transformed over time, with a one dimensional scan determining digital audio output, that is, dynamic wave terrain synthesis (Mitsuhashi 1982b, Borgonovo and Haus 1986). In the work here, we restrict ourselves to the case of the time amplitude curves of traditional break-point interpolation synthesis which will be sampled for digital audio. The key-frame approach is a widely used paradigm originating in hand animation, especially familiar in computer graphics animation. Break-point set interpolation algorithms allow the interpolation of user defined key-frames. The 2 user becomes the chief animator, and the computer automates the drudgery of inbetweening. We gain an automatic synthesis technique that allows immediate control of low-level wave shapes, whilst maintaining continuous transformation within sound, a quality well known as necessary for dynamic audio. As we shall see, most interpolation algorithms one could construct are distinct from the standard all-pervasive cross-fade. The time-amplitude break-point sets are defined within the space [0, 1] by [-1, 1], so are immediately scalable as floating point audio. We allow free values of abscissa and ordinate, though there must be only one break-point for a given value of the abscissa. Each break-point set must include at least two break-points at (0, 0) and (1, 0). This maintains continuity between successive concatenated break-point sets, and in audio terms, avoids clicks every period. Classic …