Multiple Pitch Estimation Using Non-Homogeneous Poisson Processes

Novel statistical models are proposed and developed in this paper for automated multiple-pitch estimation problems. Point estimates of the parameters of partial frequencies of a musical note are modeled as realizations from a non-homogeneous Poisson process defined on the frequency axis. When several notes are combined, the processes for the individual notes combine to give a new Poisson process whose likelihood is easy to compute. This model avoids the data-association step of linking the harmonics of each note with the corresponding partials and is ideal for efficient Bayesian inference of unknown multiple fundamental frequencies in a signal.