Audio cross-fade implementation via rational functions

Implementation of the cross-fade audio effect requires shaping the fade profile for a certain audio content that is to be faded out, as well as customizing the audio fade for an additional audio content, which is to be faded in, with the purpose of achieving a smooth transition between the two different audio contents. Similar to the case of applying adjustable fades, the audio cross-fades are usually carried out in the off-line mode, by employing various transcendental functions to shape the audio fades (both fade-out and fade-in effects). To improve the computational capabilities by minimizing the delay between receiving the position within the cross-fade effect and returning both the volume of the faded out section and the volume of the faded in one, we consider that, during the cross-fade effect, the audio volume of each of the two overlapping sections is the output of a rational function i.e. a mapping defined by a rational fraction. A plain HTML5/JavaScript implementation, prepared to be tested in any major browser, is advanced in the paper in order to highlight the suitability of the suggested approach to audio cross-fade customization with real-time computing.