Online Estimation of Multiple Harmonic Signals

In this paper, we propose a time-recursive multipitch estimation algorithm using a sparse reconstruction framework, assuming that only a few pitches from a large set of candidates are active at each time instant. The proposed algorithm does not require any training data, and instead utilizes a sparse recursive least-squares formulation augmented by an adaptive penalty term specifically designed to enforce a pitch structure on the solution. The amplitudes of the active pitches are also recursively updated, allowing for a smooth and more accurate representation. When evaluated on a set of ten music pieces, the proposed method is shown to outperform other general purpose multipitch estimators in either accuracy or computational speed, although not being able to yield performance as good as the state-of-the art methods, which are being optimally tuned and specifically trained on the present instruments. However, the method is able to outperform such a technique when used without optimal tuning, or when applied to instruments not included in the training data.