HRLib: sinusoid/noise separation in audio signals
By O. Gillet

HRLib library, developed by Olivier Gillet, is a C implementation of a sinusoid/noise separation method from Roland Badeau’s Thesis [1]. A graphical interface permits to perform separation and mix of separated tracks in real time.

The audio signal is decomposed into a sum of exponentially damped sinusoids (EDS) and autoregressive noise. This decomposition is based on the high-resolution subspace method ESPRIT. Initially, the signal is pre-accentuated, and then decomposed into sub-bands. In each channel, the noise autoregressive envelope is estimated, and the signal is whitened with a FIR Filter [1].

It uses the ESTER method [2] to estimate the number of sinusoids, and a fast adaptive algorithm (Sequential Iteration) for subspace tracking [3]. Sinusoids/noise separation is performed by projection onto the signal subspace and the noise subspace [4], and by reconstruction with the synthesis filter bank.


  • contact roland.badeau (at)


  1. Méthodes à haute résolution pour l'estimation et le suivi de sinusoïdes modulées. Application aux signaux de musique. R. Badeau. Thèse de l'ENST soutenue le 18 avril 2005. Prix de thèse ParisTech 2006.
  2. A new perturbation analysis for signal enumeration in rotational invariance techniques, R. Badeau, B. David et G. Richard, IEEE Trans. on Signal Proc., vol. 54, no. 2, pp. 450-458, février 2006.
  3. EDS parametric modeling and tracking of audio signals, R. Badeau, R. Boyer et B. David, Proceedings of the 5th International Conference on Digital Audio Effects (DAFx-02), Hambourg, Allemagne, 26-28 septembre 2002, pp. 139-144.
  4. An EDS modelling tool for tracking and modifying musical signals, B. David, G. Richard et R. Badeau, Stockholm Music Acoustics Conference (SMAC 2003), Stockholm, Suède, 6-9 août 2003, vol. II, pp. 715-718.