An Overview of Pitch Detection Algorithms Alexandre Savard

Content • Introduction – Classification – Applications – Problems and Constraints • Time Domain

Introduction Prior Definitions – Pitch : Defined as the perceptual appreciation of the highness

Introduction Application of Pitch Tracking – Music Automatic Transcription from audio signals to common

Introduction Non-Exclusive Classification – Voice ( Speech, Singing ) – Instrumental – Monophonic –

Introduction Generally Encountered Problems – Noise – Reverberation – Other Sounds from the environment

Introduction Music-Specific Difficulties – Large frequency range for musical instrument – Many instrumental sound

Time Domain • Zero-Crossing Detection • Autocorrelation Function • Average Magnitude Difference Function Template

Time Domain Zero-Crossing Detection – Based on a direct application of the definition of

Time Domain Zero-Crossing Detection http: //www-ccrma. stanford. edu/~pdelac/154/m 154 paper. htm#_ftn 5 Template copyright

Time Domain Autocorrelation Technique – Cross-Correlation is a non-linear operation that measure the similarity

Time Domain Autocorrelation Technique – Autocorrelation is a cross-correlation of a signal with itself.

Time Domain Autocorrelation Technique Template copyright 2005 http: //www. phon. ucl. ac. uk/courses/spsci/matlab/lect 10.

Time Domain Autocorrelation Technique – Not very efficient for high fundamental frequency. – Convolution

Time Domain Average Magnitude Difference Function – It is an alternate to Autocorrelation function.

Time Domain Other Temporal Algorithm – Waveform Maximum Detection – Sum Magnitude Difference Squared

Time Domain Other Temporal Algorithm – Adaptive Filter – Super Resolution Pitch Determination Template

Frequency Domain • Harmonic Product Spectrum • Cepstrum Template copyright 2005 www. brainybetty. com

Frequency Domain Harmonic Product Spectrum – FFT is used to convert temporal representation of

Frequency Domain Harmonic Product Spectrum – The highest peak most likely correspond to the

Frequency Domain Harmonic Product Spectrum – Presents a high degree of robustness in a

Frequency Domain Cepstrum – Cepstrum is defined as the inverse Fourrier transform of the

Frequency Domain Calculation of Cepstrum for Voice – In the source filter-model, voiced speech

Frequency Domain Cepstrum – The logarithim operation flatten the spectra so that it gives

Frequency Domain Other Frequency Domain Algorithm – Maximum Likelihood – Linear Prediction Coding –

Alternative Technique Teager Energy Function – Referring again to the source-filter model for voice,

Alternative Technique Teager Energy Function – The Teager energy function is a non-linear operator

Alternative Technique Miscellaneous Technique – Wavelet Transform – Bayesian Statistical Model – Hidden Markov

Conclusion Template copyright 2005 www. brainybetty. com

Bibliography • Liu B. , Wu Y. , L Yi. "Linear Hidden Markov Model

Bibliography • Luo H. , Denbigh P. "A Speech Separation System That Is Robust

Bibliography • Marchand S. "An Efficient Pitch-Tracking Algorithm Using a Combination of Fourier Transforms.

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Content • Introduction – Classification – Applications – Problems and Constraints • Time Domain Algorithms • Frequency Domain Algorithms • Alternative Techniques • Conclusion Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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 timescaling operation Template copyright 2005 www. brainybetty. com

Introduction Non-Exclusive Classification – Voice ( Speech, Singing ) – Instrumental – Monophonic – Polyphonic – Time-Based Algorithm – Spectral-Based Algorithm – Alternative Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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 timeshifted 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 Template copyright 2005 similarity. www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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 Nlog. N. – 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. Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

Frequency Domain Harmonic Product Spectrum – The highest peak most likely correspond to the fundamental frequency Template copyright 2005 http: //www-ccrma. stanford. edu/~pdelac/154/m 154 paper. htm#_ftn 5 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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: Template copyright 2005 www. brainybetty. com

Frequency Domain Cepstrum – The logarithim operation flatten the spectra so that it gives more robustness formants – However this same operation rises the noise level Template copyright 2005 www. brainybetty. com

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 Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

Alternative Technique Miscellaneous Technique – Wavelet Transform – Bayesian Statistical Model – Hidden Markov Model – Graphical probablilistic Models – Perceptual Pitch Detector Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com

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. Template copyright 2005 www. brainybetty. com