Combining Zeroth and First-Order Analysis with Lagrange Polynomials to Reduce Artefacts in Live Concatenative Granulation

This paper presents a technique addressing signal discontinuity and concatenation artefacts in real-time granular processing with rectangular windowing. By combining zero-crossing synchronicity, first-order derivative analysis, and Lagrange polynomials, we can generate streams of uncorrelated and non-overlapping sonic fragments with minimal low-order derivatives discontinuities. The resulting open-source algorithm, implemented in the Faust language, provides a versatile real-time software for dynamical looping, wavetable oscillation, and granulation with reduced artefacts due to rectangular windowing and no artefacts from overlap-add-to-one techniques commonly deployed in granular processing.