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Audio Signal Classification Rough-Sets based Approach

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Audio Signal ClassificationRough-Sets based Approach

- Introduction - the research goals
- Musical instrument acoustics
- Parameters of sounds and their separability
- Preprocessing for rough set tools: discretization (quantization) of parameters
- Automatic classification and results
- Summary

- Motivation – to deal with the problem of the automatic classification of musical data:
- database searching: there is no possibility to find fragments performed by selected instruments inside files, unless such information is attached to the file

- Aim – to check if it is possible to recognize sounds on the basis of a limited number of parameters, and reveal these parameters

?

- Amount of data in sound files
1 s, Fs=44.1kHz, 16 bits stereo, 176.4 kB

- Musical instrument sound data are unrepeatable and inconsistent:
- the sound depends on the articulation, the instrument itself, arrangement of microphones, reverberation, etc.
- sounds of different instruments can be similar, whereas sounds of one instrument may change significantly within the scale of the instrument

- articulation:
- bowed vibrato, muted/not muted,
- pizzicato (string plucked),

- sound:
- body resonances
- inharmonic partials:
where f1- fundamental (pitch)

- pizzicato: transients only

- articulation - vibrato/non vibrato
- the length of the horn resonator is reduced by holes between the mouthpiece and the end
- reed instruments – excited by vibrating reeds :
- single reed: clarinet, saxophone
- double reed: oboe, English horn, bassoon

- flute:
- blowing a stream of air across a hole in the body

- articulation: vibrato, muted/not muted
- lip-driven
- mouthpieces only help with tone production
- long narrow body and extended flaring end - upper modes available
- mechanical valves

- consequent sounds in the musical scale of instruments
- source - CD: McGill University Master Samples
- stereo, sampling frequency 44.1 kHz, 16 bits

- Fourier analysis:

- example: oboe, 440 Hz

A

partials (harmonics)

f

- The spectrum changes with time evolution

t - starting transient

qs - quasi-steady state

time envelope of an exemplary sound

- fdm– mean frequency deviation for low partials
- hfd_max=1..5 – a partial with the greatest frequency deviation
- A1-2 [dB] – amplitude difference between 1st and 2nd partial,
- h1, h3,4,h5,6,7, h8,9,10, hrest –
- energy of the selected partials
- Od, Ev – contents of odd/even partials in the spectrum
- Br– brightness of the sound:

- f 1 [Hz] – fundamental
- |f1max– f1min| – vibrato,
- dfr – fractal dimension of the spectrum envelope:
- where N(r) - minimal number of squares r covering the envelope,

- criterion:

Di,j

– measure of distances between classesi, j

- Hausdorff metrics

- max/min/mean distance between objects
- from different classes

– measure of dispersion in classi

di

- mean/max distance between class objects or
- from the gravity center of the class

- set of parameters is satisfying if Q>1

- definition:

- Euclidean

- “city”

- central

d1/d2 - mean/max distance

between class objects

d3/d4 - mean/max distance

from the gravity center

D1 - Hausdorff metric

D2/D3/D4 - max/min/mean

distance between objects

from different classes

- inductive learning methods require a small number of attribute values
- global methods: simultaneously convert all continuous attributes – large tables
- Boolean approach (Skowron, Nguyen)
- cluster analysis (Chmielewski, Grzymala-Busse)

- local methods: restricted to simple attributes
- methods usually do not discern between points representing different classes

- equal interval width method (EIWM)

- maximum distance method (MDM)

- statistical clusterization

Let – a decision table

U - a universe - nonempty, finite set of objects

A - a nonempty, finite set of attributes

,

the decision attribute

implies indiscernibility relation IND(B)

reduct - aminimal subset B such that IND(A)=IND(B)

– lower approximation

of X in A

– upper approximation

of X in A

rough set in A - the family of all subsets of U

having the same lower and upper approximations in A

- B positive region of A

- the generalized decision inA

B - relative reduct iff B is a minimal subset of A

such that

The relative reduct is such minimal subset of A

which preserves the positive region

- generated rules

where n - length of the rule

- a rough measure m of the rule describing concept X

Y – set of all examples described by the rule

- LERS
- allows unknown attribute values
- possibility of removing inconsistent examples (i.e. of identical attribute values, but with different decisions)
- priority of attributes is controlled

- DataLogic
- calculates attribute and rule strength
- quantization of data is available

- implemented in Mathematica
- allows data quantization with number of methods, both local and global
- ten-fold test included
- priority of attributes is controlled
- unnecessary attributes found by reducts and relative calculation
- the use of produced rules available for whole data sets, not only for singular objects

reduct

relative reduct 1

relative reduct 2

- up to 70% correct recognition obtained in RS tests

- parameters 60,61,62 and 41,44,30,55 are the most significant

- the huge amount of data contained in digital sound representation requires parametrization as preprocessing
- a great number of parameters is a consequence of the variety of musical instruments and differences in their sounds
- inconsistency of the data implies soft computing techniques for automatic classification
- quantization is necessary as preprocessing for RS algorithms

- an appropriate choice of the quantization requires many experiments
- rough set algorithms allow the evaluation of the significance of parameters
- composition of parameters in RS reducts confirms that the evolution of the sound must be taken into account during parametrization
- the use of learning algorithms allows finding rules for managing classification