Music Analysis

Josiah Boning

TJHSST Senior Research ProjectComputer Systems Lab, 2007-2008

Purpose Framework for study of audio data Components:

Statistical Signal Processing Machine Learning

Uses: Aircraft identification Speech recognition and synthesis And more...

Ideal: computer recognition of music

Background

Bigarelle and Iost (1999) Music genre can be identified by fractal dimension

Basilie et al. (2004) Music genre can be identified by machine learning

algorithms Used discrete MIDI data

Methods

Data Processing Spectral Analysis: Fourier Transform Fractal Dimension: Variation and ANAM Methods

Machine Learning Feed-Forward Neural Network

Spectral Analysis – Fourier Transform

F v =∫−∞

∞f t e−2 pi i v t dt

Time domain to frequency domain

Fourier Transform

Spectrogram

Many Fourier transforms sequentially

Frequency Aggregate

Horizontal sum of spectrogram

Magnitude Aggregate

Vertical sum of spectrogram

Can perform second Fourier transform

Fractal Dimension

lim0

2−

log 1b−a∫a

b

∣max f t ∣x−t∣−min f t

∣x−t∣ ∣dx log

lim0

2−

log 1b−a ∫

x=a

x=b [ 1

2 ∫t 1=0

∫t 2=0

∣ f xt1− f x−t 2∣dt1dt2 ]

1 /

dx log

Bigerelle and Iost – used to distinguish genre Variation Method:

ANAM Method:

Fractal Dimension

Inaccurate calculations Correct values around 1.6-1.9 Variation: ~1.16 ANAM: ~2.25

Interpolation between samples didn’t help

Machine Learning

Neural networks Feed-Forward

Neurons

Each node performs weighted, rescaled sum of input values

Scaling: Sigmoid function

f x= 11e−x

Results

Frequency aggregate – songs are similar!

Results

Magnitude and frequency: negative correlation Not shared by

white noise

Fourier transform of magnitude aggregate Meaningless

Where next?

Move code from driver to Fourier module Otherwise, well organized

Fix fractal dimension calculations Neural network learning algorithms Beat detection Other signal processing techniques