Estimation of Fundamental Frequencies in Stereophonic Music Mixtures

In this paper, a method for multi-pitch estimation of stereophonic mixtures of harmonic signals, e.g., instrument recordings, is presented. The proposed method is based on a signal model that includes the panning parameters of the sources in a stereophonic mixture, such as those applied artificially in a recording studio. If the sources in a mixture have different panning parameters, this diversity can be used to simplify the pitch estimation problem. The mixing parameters of the sources might be shared, resulting in a multi-pitch estimation problem, which is solved using an approach based on an expectation-maximization algorithm for Gaussian sources, where the fundamental frequencies and model orders are estimated jointly. The fundamental frequencies may be related, resulting in overlapping harmonics, complicating the estimation of the parameters. A codebook of harmonic amplitude vectors is trained on recordings of instruments playing single notes, and used when estimating the amplitudes of the mixture components. The proposed method is evaluated using stereophonic mixtures of instrument recordings and is compared to state-of-the-art transcription and multi-pitch estimation methods. Experiments show an increase in performance when knowledge about the panning parameters is taken into account. The proposed method provides a full parameterization of the components of the observed signal. Possible applications include instrument tuning, audio editing tools, modification of harmonic mixture components, and audio effects.