Pitch-Synchronous Multiresolution Analysis of Music Signals

In this thesis a novel multiresolution approach for note detection in a polyphonic mix is proposed. The idea is to use a set of wavelets whose lengths are adapted to the theoretical fundamental period of musical notes. Using the typical wavelet dyadic decomposition we can generate a set of wavelets that match the fundamental frequency (F0) of a given note in every octave. Therefore, using a set of 12 different wavelets, one per each semitone, we can represent the fundamental frequency of every note in every octave using one wavelet scale per each octave. The magnitude and phase continuity of wavelet coefficients across temporal frames is exploited to draw a special kind of spectrogram, namely Pitch-Synchronous Wavelet Spectrogram (PSWS). When the corresponding F0 and harmonics of a note are present in the signal, a special DC pattern appears in the PSWS, due to the aforementioned continuity. Any other harmonic signal or noise produces pseudo-periodic or random AC patterns. This way, by filtering the AC components, we can identify the DC patterns in the PSWS and state the presence of a given musical note at some moment in time, even if the signal is polyphonic. For the moment, the method only works satisfactorily when the harmonic peaks in the music signal are close to the theoretical position of the frequencies of the musical notes. Some techniques are suggested in order to improve the system and extend it to non-stable pitch musical instruments.