1. Extracting Individual Tracks from Polyphonic Music
Nick Starr, Computer Systems Lab

2. Source Separation • "Cocktail Party" analogy
• Magnetoencephalography (MEG) - Brain imaging with magnetic fields
• Music

3. Source Separation (cont)
x = Observed
s = Source
a = Mixing constants
• x is known
• a can be computed
• With x and a known, s can be solved for

4. Methods of Source Separation
• Principal Components Analysis
• Computational Auditory Scene Analysis
• Independent Component Analysis

5. Fourier Transforms

6. Fourier Transforms (cont)
The Math:
The Explanation:
• Maps domain from time to frequency
• Easily invertible
• Many different computational techniques

7. Fourier Transforms (cont)

8. Independent Component Analysis
• Decomposition
    • Fourier Transform, separate moduli and phases
    • Matrices, matrices, matrices
• Classification
    • Center of research
    • Separate important parts from unimportant
• Recombination
    • Bring back the phases
    • Combine with classified moduli
    • Inverse Fourier Transform

9. Results
Segmentation fault

10. Challenges
• Understanding the math
• C and GSL
• Mathematica File I/O

11. Questions?