Instrument Timbres and Pitch Estimation in PolyphonicMusic

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This text connects essential knowledge about music and human auditory perception with signal processing algorithms to solve the specific problem of pitch estimation. The designed algorithm obtains an estimate of the magnitude spectrum via STFT and models the harmonic structure of each pitch contained in the magnitude spectrum with Gaussian density mixtures, whose parameters are subsequently estimated via an Expectation-Maximization (EM) algorithm. Heuristics for EM initialization are formulated mathematically. A prototype was implemented in MATLAB, featuring a GUI that provides for visual (spectrogram) and numerical (console) verification of results. The algorithm was tested using an array of data ranging from single to triple superposed instrument recordings. Its advantages and limitations are discussed, and a brief outlook over potential future research is given.