Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription

This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci

Learning Opportunities 2015/2016

The graduation requirements of the Illinois Mathematics and Science Academy are in concert with those maintained by the State of Illinois with additional requirements as established by the IMSA Board of Trustees. Each semester students must take a minimum of 5 academic courses (2.5 credits) for a grade (not Pass/Fail). Fine Arts, Wellness, and Independent Study courses, or any course taken on a Pass/Fail basis do not count towards the 5 course (2.5 credits) minimum. Most students will take between 5 (2.5 credits) and 7 (3.5 credits) academic courses per semester. Only courses taken for a letter grade will count towards graduation credit. Students who take more than 5 academic courses may choose to take all courses for a grade. It is recommended that students who are approved to take 7 academic courses declare one elective Pass/Fail

A User-assisted Approach to Multiple Instrument Music Transcription

PhDThe task of automatic music transcription has been studied for several decades and is regarded as an enabling technology for a multitude of applications such as music retrieval and discovery, intelligent music processing and large-scale musicological analyses. It refers to the process of identifying the musical content of a performance and representing it in a symbolic format. Despite its long research history, fully automatic music transcription systems are still error prone and often fail when more complex polyphonic music is analysed. This gives rise to the question in what ways human knowledge can be incorporated in the transcription process. This thesis investigates ways to involve a human user in the transcription process. More specifically, it is investigated how user input can be employed to derive timbre models for the instruments in a music recording, which are employed to obtain instrument-specific (parts-based) transcriptions. A first investigation studies different types of user input in order to derive instrument models by means of a non-negative matrix factorisation framework. The transcription accuracy of the different models is evaluated and a method is proposed that refines the models by allowing each pitch of each instrument to be represented by multiple basis functions. A second study aims at limiting the amount of user input to make the method more applicable in practice. Different methods are considered to estimate missing non-negative basis functions when only a subset of basis functions can be extracted based on the user information. A method is proposed to track the pitches of individual instruments over time by means of a Viterbi framework in which the states at each time frame contain several candidate instrument-pitch combinations. A transition probability is employed that combines three different criteria: the frame-wise reconstruction error of each combination, a pitch continuity measure that favours similar pitches in consecutive frames, and an explicit activity model for each instrument. The method is shown to outperform other state-of-the-art multi-instrument tracking methods. Finally, the extraction of instrument models that include phase information is investigated as a step towards complex matrix decomposition. The phase relations between the partials of harmonic sounds are explored as a time-invariant property that can be employed to form complex-valued basis functions. The application of the model for a user-assisted transcription task is illustrated with a saxophone example.QMU