Pitch Recognition with Wavelets

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Pitch Recognition with Wavelets

• 1.130 Final Presentation
• by Stephen Geiger

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What is pitch recognition?

• Well, what is pitch? . . .
• How HIGH or LOW a sound is
• Which note?
• Perceived Frequency

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Relationship Between Pitch and Frequency
Pitch
Fundamental Frequency
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For Example

• For Middle C

Frequency 262 Hz
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For an A Scale
A 2202(0/12) 220 Hz A 2202(1/12) 233
Hz B 2202(2/12) 247 Hz C 2202(3/12) 262
Hz C 2202(4/12) 277 Hz D 2202(5/12) 294
Hz D 2202(6/12) 311 Hz
E 2202(7/12) 330 Hz F 2202(8/12) 349
Hz F 2202(9/12) 370 Hz G 2202(10/12)
392 Hz G 2202(11/12) 415 Hz A
2202(12/12) 440 Hz
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An Octave Up

• For C5

Frequency 524 Hz
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A Sum with 2 Frequencies
Frequency 262 Hz and Frequency 524 Hz
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Freq in a Piano - Middle C
Frequency, Hz
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FFT of a Oboe Middle C
Frequency, Hz
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Mono vs. Poly

• Monophonic
• one note at a time
• (e.g. trumpet)
• Polyphonic
• multiple notes at a time
• (e.g. piano, orchestra)

Creates a problem for pitch recognition. (especial
ly octaves!)
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Some Existing Methods

• Time Domain Pitch Period estimation
• With wavelets.
• With auto-correlation function.
• Freq. Domain Find Fundamental
• Auditory Scene Analysis
• Blackboard Systems
• Neural Networks
• Perceptual Models

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What applications are there?

• Transcription of Music
• Modeling of Musical Instruments
• Speech Analysis
• Besides its an Interesting Problem

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• My Work . . .

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A Novel Wavelet Approach
Based on an observation made by Jeremy Todd,
that
For a piano playing these notes, a CWT could be
used to identify a G with certain scale/wavelet
combinations. Even with some polyphony !
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Finding a G in a C Scale
Original Signal
CWT _at_ Specific Scale
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The Continuous Wavelet Transform

• Definition of a CWT

Where a scaling factor
b shift factor f(t) function
we start with Y(t) Mother wavelet
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What is Scale?
LOW SCALE Compressed Wavelet Lots of Detail High
Frequency
HIGH SCALE Stretched Wavelet Coarse Features Low
Frequency
(You are here)
(And here)
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Gaussian 2nd Order Wavelet
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Initial Work

• Took an empirical approach.
• Ran a number of CWTs at varying scale, and
  looked at the results.
• Picked out a CWT scale for each note in the C
  scale.

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Finding Notes in a C Scale
Original
Scale 594 530 472 446 394 722 642 606
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Finding Notes w/ Polyphony
Original
Scale 594 530 472 446 394 722 642 606
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More Complex Polyphony
Original Scale 594 530 472 446 394 722 642 606
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Testing with different timbre
Original
Scale 594 530 472 446 394 722 642 606
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Why does this work?

• The scale parameter
• in the CWT affects
• frequency response.
• However, our scales that
• work dont seem to follow
• a clear pattern.

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Training Algorithm

• Again, took an empirical approach.
• Ran CWTs at varying scales,
• on sample files containing one note.
• Picked out scales, where
• maximum of the CWT for
• one note gtgt other notes
• (and collected results).

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• Results of
• Training Algorithm
• . . .

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Longer C Scale Trained on 3 Octaves of Notes
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A Fragment by Chopin
From Right Hand of Prelude in C, Op. 28 No. 1
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Training on a Real Guitar

• Only able to find 5 of 8 pitches for C Scale
  training case. (With limited attempt).
• Results on a test file were not completely
  accurate.
• Expected to be a more difficult case than a
  piano.
• Could merit a more thorough try.

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Entire 88 K on a P

• Work in progress.
• It takes a long time to run many CWTs on 88
  different sound files.
• Initial results able to
• identify notes 70-88.

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Frequency Response Revisited
Frequency Response of a 2nd Order Gaussian Wavelet
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Resulting Scales for 22 Piano Notes
SCALE
NOTE NUMBER
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Resulting Scales for 8 Sinusoidal Notes
SCALE
NOTE NUMBER
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Conclusions

• The novel wavelet approach isnt perfect.
• Requiring training is a handicap.
• Most likely not suited to sources with varying
  timbre. (e.g. guitar, voice)
• Some interesting results.
• The mechanism of detection could be further
  investigated and better understood.