Harmonics Plus Noise Model

We now propose a method for considering a harmonics plus noise model of each input source in cases where DASSS suggests that more than one source is present. Though this method has not yet been implemented, we plan to pursue this approach in the weeks to come. We will require that the spectral content of each source be either:

• harmonic, meaning that the spectral components are integer multiples of a single fundamental frequency, or
• bandlimited noise-like, meaning that the spectral components are part of a spectrally smooth curve.

To introduce this source model into the current paradigm, we will allow the calculation of source components via equation 7 only when the sources satisfy the above requirements. This decision clearly requires estimates of the fundamental frequency and bandlimited noise shape of each source. To determine the former, we can use any of a variety of pitch detection techniques on the source signals estimated using the single source approach of section 4. Although music signals are characterized by large overlap of spectral components, even a few spectral peaks may yield a reliable pitch estimate. Furthermore, the pitch detection data may be smoothed over frames, or considered across source estimates so as to seek at least say $N$ pitches. To determine the overall noise shape, similar techniques may be employed. Given these estimates for each source, we will develop a scoring function to determine how likely it is that a particular bin belongs to a given source. If the function scores above a certain threshold, we will include the corresponding source in an inverse or pseudo-inverse calculation similar to equation 7. We note that the harmonics plus noise model is only minimally constrained, and that most speech and non-percussive instrument sounds may be modeled this way. We currently place no constraints on the smoothness of the harmonics' spectral envelope or the pitch range of the fundamental frequency. These characteristics tend to be instrument or voice-gender specific, and have been exploited to significant pitch detection success in [4]. Nonetheless, we maintain the generality, flexibility, and simplicity of the model by avoiding such considerations for the present.