Note-event Detection in Polyphonic Musical Signals based on Harmonic Matching Pursuit and Spectral Smoothness
Francisco Jesus Canadas-Quesada, Pedro Vera-Candeas, N. Ruiz-Reyes, R. Mata-Campos, Julio J. Carabias-Orti · Journal of New Music Research · 2008
Harmonic Matching Pursuit (HMP) is an interesting signal processing tool to detect simultaneous notes in musical audio signals. HMP decomposes an audio signal into harmonic atoms, a suitable choice due to their strong harmonic content. However, HMP provides an inaccurate decomposition when notes with a rational frequency relation are simultaneously played (the overlapping partial problem). An example of such a situation is the common occurrence in Western music of consonant intervals, i.e. perfect fifth (3:2), perfect fourth (4:3) or major third (5:4). For these cases, HMP often obtains harmonic atoms whose fundamental frequencies are the greatest common divisor of the active fundamental frequencies. To solve this problem, we propose a processing algorithm that works over the harmonic atoms obtained by HMP. This algorithm is based on maximizing the smoothness of the spectral envelope for each harmonic atom provided by the HMP decomposition. Results show that our proposal achieves a good performance. Competitive accuracy and error measures in a musical transcription application are reported in relation to the state of the art transcription systems.