Harmonic Bandwidth Companding for Separation of Overlapping Harmonics in Pitched Signals

We present a novel approach to separating pitched signals from single-channel mixtures by harmonic bandwidth companding. Recalling that in a short analysis window the harmonic waveform envelope conveys information about approximate amplitude and frequency time variations, we show that proper linear waveform envelope smoothing reduces frequency spread around the harmonics and thus compresses the harmonic bandwidth. Such an action largely relaxes worst-case separation scenarios, which are caused by large proportions of overlapped harmonics. The distortion in separated signals due to harmonic bandwidth compression is compensated by an inverse system—the harmonic bandwidth expander. The benefit of such an approach is that explicit classification in overlapped and non-overlapped harmonics is no longer needed. Moreover, the underlying signal model is linear-in-parameters which allows for an efficient estimation via linear least-squares. The results show that harmonic bandwidth companding significantly outperforms two state-of-the-art separation methods.