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A reformulation of Prior Subspace Analysis (PSA) is presented, which restates the problem as that of fitting an undercomplete signal dictionary to a spectrogram. Further, a generalization of PSA is derived which allows the transcription of polyphonic pitched instruments. This involves the translation of a single frequency prior subspace of a note to approximate other notes, overcoming the problem of needing a separate basis function for each note played by an instrument. Examples are then demonstrated which show the utility of the generalised PSA algorithm for the purposes of polyphonic pitch transcription.
Fitzgerald, D., Cranitch, M., Coyle, E.: Generalised prior subspace analysis for polyphonic pitch transcription. Proceedings of the 8th. International Conference on Digital Audio Effects (DAFX05), Madrid, Spain, 2005.