Many music signals can largely be considered an additive combination ofmultiple sources, such as musical instruments or voice. If the musical sourcesare pitched instruments, the spectra they produce are predominantly harmonic,and are thus well suited to an additive sinusoidal model. However,due to resolution limits inherent in time-frequency analyses, when the harmonicsof multiple sources occupy equivalent time-frequency regions, theirindividual properties are additively combined in the time-frequency representationof the mixed signal. Any such time-frequency point in a mixturewhere multiple harmonics overlap produces a single observation from whichthe contributions owed to each of the individual harmonics cannot be triviallydeduced. These overlaps are referred to as overlapping partials or harmoniccollisions. If one wishes to infer some information about individual sources inmusic mixtures, the information carried in regions where collided harmonicsexist becomes unreliable due to interference from other sources. This interferencehas ramifications in a variety of music signal processing applicationssuch as multiple fundamental frequency estimation, source separation, andinstrumentation identification.This thesis addresses harmonic collisions in music signal processing applications.As a solution to the harmonic collision problem, a class of signalsubspace-based high-resolution sinusoidal parameter estimators is explored.Specifically, the direct matrix pencil method, or equivalently, the Estimationof Signal Parameters via Rotational Invariance Techniques (ESPRIT)method, is used with the goal of producing estimates of the salient parametersof individual harmonics that occupy equivalent time-frequency regions. Thisestimation method is adapted here to be applicable to time-varying signalssuch as musical audio. While high-resolution methods have been previouslyexplored in the context of music signal processing, previous work has notaddressed whether or not such methods truly produce high-resolution sinusoidal parameter estimates in real-world music audio signals. Therefore, thisthesis answers the question of whether high-resolution sinusoidal parameterestimators are really high-resolution for real music signals.This work directly explores the capabilities of this form of sinusoidal parameterestimation to resolve collided harmonics. The capabilities of thisanalysis method are also explored in the context of music signal processingapplications. Potential benefits of high-resolution sinusoidal analysis areexamined in experiments involving multiple fundamental frequency estimationand audio source separation. This work shows that there are indeedbenefits to high-resolution sinusoidal analysis in music signal processing applications,especially when compared to methods that produce sinusoidalparameter estimates based on more traditional time-frequency representations.The benefits of this form of sinusoidal analysis are made most evidentin multiple fundamental frequency estimation applications, where substantialperformance gains are seen. High-resolution analysis in the context ofcomputational auditory scene analysis-based source separation shows similarperformance to existing comparable methods.
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