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An Overview of Pitch Detection Algorithms. Alexandre Savard MUMT611: Music Information Acquisition, Preservation, and Retrieval February 2006. Content. Introduction Classification Applications Problems and Constraints Time Domain Algorithms Frequency Domain Algorithms

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An Overview of Pitch Detection Algorithms

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An Overview of Pitch Detection Algorithms

Alexandre Savard

MUMT611: Music Information Acquisition, Preservation, and Retrieval

February 2006

Content

Introduction

Classification

Applications

Problems and Constraints

Time Domain Algorithms

Frequency Domain Algorithms

Alternative Techniques

Conclusion

Introduction

Prior Definitions

Pitch : Defined as the perceptual appreciation of

the highness or the lowness of a sound. It is related

to the periodicity of a sound.

Frequency : Physical attribute of a sound or any

type other of signal. Describes the amount of times

that a repeated event occur per unit of time.

Fundamental Frequency :In a complex sound or

signal, it is the lowest partial.

Introduction

Application of Pitch Tracking

Music Automatic Transcription from audio signals to

common music notation or to MIDI number

Score Following

Musical Queries by singing or humming

Acoustic feature for Human-Computer Interaction

Sound-Editing Program like pitch-shifting and time-

scaling operation

Introduction

Non-Exclusive Classification

Voice ( Speech, Singing )

Instrumental

Monophonic

Polyphonic

Time-Based Algorithm

Spectral-Based Algorithm

Alternative

Introduction

Generally Encountered Problems

Noise

Reverberation

Other Sounds from the environment

Shortness of the sustained part for certain sounds

Sounds need to be analyzed right after the attack

transient where they are not totally stable

Detuning during the sustain part of a sound

Minimal output delay for realtime.

Introduction

Music-Specific Difficulties

Large frequency range for musical instrument

Many instrumental sound have inharmonic partials

Expressiveness factors ( glissando, vibrato, thrill )

Fast algorithm for real-time processing

Multiphonic

Time Domain

Zero-Crossing Detection

Autocorrelation Function

Average Magnitude Difference

Function

Time Domain

Zero-Crossing Detection

Based on a direct application of the definition of

periodicity

Counting the number of time that the signal crosses a

reference level

Mostly Inexpensive in computation

Weakness against noise

Presents weakness when used to analyze signals with

energy in high frequencies

Time Domain

Zero-Crossing Detection

http://www-ccrma.stanford.edu/~pdelac/154/m154paper.htm#_ftn5

Time Domain

Autocorrelation Technique

Cross-Correlation is a non-linear operation that

measure the similarity between two signal.

The coresponding samples of a signals and a time-

shifted version of an other one are multiplied and

added toghether.

The Cross-Correlation functionwill then have a peak to

the offset value which coresponds to the maximum of

similarity.

Time Domain

Autocorrelation Technique

Autocorrelation is a cross-correlation of a signal with

itself.

The maximum of similarity occurs for time shifting of

zero.

An other maximum should occur in theory when the

time-shifting of the signal corresponds to the

fundamental period.

Time Domain

Autocorrelation Technique

http://www.phon.ucl.ac.uk/courses/spsci/matlab/lect10.html

Time Domain

Autocorrelation Technique

Not very efficient for high fundamental frequency.

Convolution is a very expensive process.

Computation efficiency can be improved using the FFT

algorithm instead of convolution. It reduces calculation

from N squared to NlogN.

Most of the variation of this technique related to the

mathematical definition of the autocorrelation used, the

way the maximums are localized, and how errors in the

maximum identification are attenuated.

Time Domain

Average Magnitude Difference Function

It is an alternate to Autocorrelation function.

It compute the difference between the signal and a

time-shifted version of itself.

While auttocorelation have peaks at maximum

similarity, there will be valleys in the average

magnitude difference function.

Time Domain

Other Temporal Algorithm

Waveform Maximum Detection

Sum Magnitude Difference Squared Function

Average Squared Difference Function

Cumulative Mean Normalized Difference Function

Circular Average Magnitude Difference Function

Adaptive Filter

Time Domain

Other Temporal Algorithm

Adaptive Filter

Super Resolution Pitch Determination

Frequency Domain

Harmonic Product Spectrum

Cepstrum

Frequency Domain

Harmonic Product Spectrum

FFT is used to convert temporal representation of

sound into its spectral representation

Assume that all signals are made of harmonic partials

The spectrum is compressed by a factor corresponding

to harmonic numbers

Multiplying the compressed spectrum with the

original one leads to a amplification of the fundamental

frequency

Frequency Domain

Harmonic Product Spectrum

The highest peak most likely correspond to the

fundamental frequency

http://www-ccrma.stanford.edu/~pdelac/154/m154paper.htm#_ftn5

Frequency Domain

Harmonic Product Spectrum

Presents a high degree of robustness in a noisy

environment

Less efficient for sounds that are not made from

harmonic components

Computationnally inexpensive

Octave Errors can occur

Frequency Domain

Cepstrum

Cepstrum is defined as the inverse Fourrier transform

of the logarithm of the power spectrum of a signal

Cepstrum extracts periodicity from the spectrum

It can be unformally mathematically written as:

It results a peak which correspond to the fundamental

period

Frequency Domain

Calculation of Cepstrum for Voice

In the source filter-model, voiced speech s(t) can be

considered as the convolution of a pulse train p(t) with

the impulse respond of the vocal tract h(t).

In the spectrum we get:

Taking the logarithm on both side we then obtain:

Frequency Domain

Cepstrum

The logarithim operation flatten the spectra so that so

that it gives more robustness for formants

However this same operation rises the noise level

Frequency Domain

Other Frequency Domain Algorithm

Maximum Likelihood

Linear Prediction Coding

Spectral Autocorrelation

Alternative Technique

Teager Energy Function

Referring again to the source-filter model for voice,

it can be represented by a pulse train filtered by the

vocal tract.

The pulse train is produced by the successive opening

and closure of the glottis.

The production of speech is closely related to the

release of energy through the glottis.

The opening/closure of the glottis result in a peak of

energy into the signal

Alternative Technique

Teager Energy Function

The Teager energy function is a non-linear operator

that defines the instantaneous energy as:

It is derived from the total energy of an oscillatory

spring-mass system.

Estimating the periodicity of energy peaks for the

signal leads to an approximation of the fundamental

frequency.

Alternative Technique

Miscellaneous Technique

Wavelet Transform

Bayesian Statistical Model

Hidden Markov Model

Graphical probablilistic Models

Perceptual Pitch Detector

Conclusion

Bibliography

Liu B.,Wu Y., L Yi. "Linear Hidden Markov Model for Music Information Retrieval Based on Humming." Paper presented at the International Conference on Acoustics, Speech, and Signal Processing 2003.

Li B., Li Y., Wang C., Tang C., Zhang E. "A New Efficient Pitch-Tracking Algorithm." Paper presented at the International Conference on Robotics, Intelligent Systems and Signal Processing 2003.

Chilton E., Evans B. "The Spectral Autocorrelation Applied to the Linear Prediction Residual of Speech for Robust Pitch Detection." Paper presented at the International Conference on Acoustics, Speech, and Signal Processing 1988.

Monti G., Sandler M. "Monophonic Transcription with Autocorrelation " Paper presented at the Conference on Digital Audio Effects 2000.

Liu J., Zheng T., Deng J. and Wu W. "Real-Time Pitch Tracking Based on Combined Smdsf." Paper presented at the Conference on Speech Communcation and Technology 2005.

Bibliography

Luo H., Denbigh P. "A Speech Separation System That Is Robust to Reverberation." Paper presented at the International Symposium on Speech, Image Processing and Neural Networks 1994.

Wu M., Wang D., Brown G. "A Multi-Pitch Tracking Algorithm for Noisy Speech." Paper presented at the International Conference on Acoustic, Speech, and Signal Processing 2002.

Nazih Abu-Shikhah Mohamed Deriche. "A Novel Pitch Estimation Technique Using the Teager Energy Function." Paper presented at the International Symposium on Signal Processing and its Applications 1999.

Picone J., Doddington G., Secrest B. "Robust Pitch Detection in a Noisy Telephone Environment." Paper presented at the International Conference on Acoustics, Speech, and Signal Processing 1987.

Quast H., Schreiner O., Schroeder R. "Robust Pitch Tracking in the Car Environment." Paper presented at the International Conference on Acoustics, Speech, and Signal Processing 2002.

Bibliography

Marchand S. "An Efficient Pitch-Tracking Algorithm Using a Combination of Fourier Transforms." Paper presented at the Conference on Digital Audio Effects 2001.

Walmsley P., Godsill S., Rayner P. "Polyphonic Pitch Tracking Using Joint Bayesian Estimation of Multiple Frame Parameters." Paper presented at the Workshop on Applications of Signal Processing to Audio and Acoustics 1999.

Zhu W., Kankanhalli M. "Robust and Efficient Pitch Tracking for Query-by-Humming." Paper presented at the Conference on Information, Communications and Signal Processing 2003.

Roads C., “The Computer Music Tutorial”, p.497-533, Boston, The MIT Press,

1996.