Extraction of Individual Tracks from Polyphonic Music Nick Starr.

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Presentation transcript:

Extraction of Individual Tracks from Polyphonic Music Nick Starr

Introduction Source Separation - general technique and field of research. Applications - Magnetic Imaging in Medicine - "Cocktail" problem in audio analysis Techniques - *Independent Component Analysis (ICA)* - Principal Components Analysis (PCA) - Independent Subspace Analysis (ISA)

Mathematical Background (summaries) 1. Matrix concepts and vocabulary 2. Short Time Fourier Transforms 3. Singular Value Decomposition 4. Source Separation

Technology Used C programming language, gcc, make: the bulk of the code. GNU Scientific Library (GSL): implementations of computationally intensive/complex mathematical routines Mathematica: simple testing of said complex mathematical routines, possibly even code if needed - interface with C?

Algorithm Description Decomposition STFT to send data to spectral domain SVD and other matrix operations to put data in usable form ICA to reduce complex signal to individual components Inverse STFT to send components back to time domain Classification Put the separated components into different categories for recombination Methods: Amplitude envelopes, machine learning?

Challenges Input: no useful libraries for decompressing most audio formats. Uncompressed WAV is the only practical option. Fourier Transforms: very complicated mathematically, many personal conventions involved in implementations which are often not clearly specified. GSL: lots of functionality, not much usability - who names their matrix multiplication method gsl_blas_dgemm()? Classification: how to develop more general classification techniques?