Pitch Tracking (音高追蹤) Jyh-Shing Roger Jang (張智星) MIR Lab (多媒體資訊檢索實驗室) CS, NTHU (清華大學 資訊工程系) jang@mirlab.org, http://mirlab.org/jang

Pitch (音高） Definition of pitch Characteristics of pitch Fundamental frequency (FF, in Hz): Reciprocal of the fundamental period in a quasi-periodic waveform Pitch (in semitone): Obtained from the fundamental frequency through a log-based transformation (to be detailed later) Characteristics of pitch Noise and unvoiced sound do not have pitch.

Pitch Tracking (音高追蹤) Pitch tracking: To compute the pitch vector of a give waveform (對整段音訊求取音高) Applications Query by singing/humming (哼唱選歌) Tone recognition for Mandarin (華語的音調辨識) Intonation scoring for English (英語的音調評分) Prosody analysis for speech synthesis (語音合成中的韻律分析) Pitch scaling and duration modification (音高調節與長度改變)

Pitch Tracking Algorithms Two categories for pitch tracking algorithms Time domain (時域) ACF (Autocorrelation function) AMDF (Average magnitude difference function) SIFT (Simple inverse filtering tracking) Frequency domain (頻域) Harmonic product spectrum method Cepstrum method

Typical Steps for Pitch Tracking Chop signals into frames (aka frame blocking) Compute pitch functions (ACF, AMDF, etc.) Determine pitch for a frame Max/min picking of the pitch function Remove unreliable pitch Via volume/clarity thresholding Smooth the whole pitch vector Via median filter, etc.

Frame Blocking Zoom in Frame size=256 points Overlap=84 points Frame rate = fs/(frameSize-overlap) = 11025/(256-84)=64 pitch/sec

ACF: Auto-correlation Function 1 128 Frame s(i): Shifted frame s(i+t): t=30 acf(30) = inner product of overlap part Pitch period 30

ACF Example 1 sunday.wav Fundamental frequency Sample rate = 16kHz Frame size = 512 (starting from point 9000) Fundamental frequency Max of ACF occurs at index 132 FF = 16000/(132-1) = 123.077 Hz

ACF Example 2 If the range of humans’ FF is [40, 1000], then we have the restriction for selecting pitch point: Min FF=40Hz  acf(fs/40:end) is not considered. Max FF=1000Hz  acf(1:fs/1000) is not considered.

Pitch Tracking via ACF Specs Playback Sampe rate = 11025 Hz Frame size = 353 points = 32 ms Overlap = 0 Frame rate = 31.25 f/s Playback soo.wav sooPitch.wav

Variations of ACF to Avoid Tapering Normalized version Half-frame shifting:

Variations of ACF to Normalize Range To normalize ACF to the range [-1 1]: This is based on the inequality:

AMDF: Average Magnitude Difference Function 1 128 Frame s(i): Shifted frame s(i+t): t=30 amdf(30) = sum of abs. difference Pitch period 30

AMDF Example sunday.wav Fundamental frequency Sample rate = 16kHz Frame size = 512 (starting from point 9000) Fundamental frequency Min of AMDF occurs at index 132 FF = 16000/(132-1) = 123.077 Hz

Variations of AMDF to Avoid Tapering Normalized version Half-frame shifting:

Combining ACF and AMDF Frame ACF AMDF ACF/AMDF

Example of Pitch Tracking

UPDUDP (1/4) UPDUDP: Unbroken Pitch Determination Using DP Goal: To take pitch smoothness into consideration : a given path in the AMDF matrix : Number of frames : Transition penalty : Exponent of the transition difference

UPDUDP (2/4) Optimum-value function D(i, j): the minimum cost starting from frame 1 to position (i, j) Recurrent formula: Initial conditions : Optimum cost :

UPDUDP (3/4) A typical example

UPDUDP (4/4) Insensitivity in

Harmonic Product Spectrum hps.m

Frequency to Semitone Conversion Semitone : A music scale based on A440 Reasonable pitch range: E2 - C6 82 Hz - 1047 Hz ( - )

Unreliable Pitch Removal Pitch removal via volume thresholding Plot by self demo of ptByPf.m

Unreliable Pitch Removal Pitch removal via volume/clarity thresholding Plot by self demo of ptByPf.m

Rest Handling With rests Without rests

Rest Handling Original pitch vectors with rests. Rests are replaced by previous nonzero pitch. Good for LS. Rests are removed. Good for DTW.

Typical Result of Pitch Tracking Pitch tracking via autocorrelation for茉莉花 (jasmine)

Comparison of Pitch Vectors Yellow line : Target pitch vector

Demo of Pitch Tracking Real-time display of ACF for pitch tracking toolbox/sap/goPtByAcf.mdl Real-time pitch tracking for real-time mic input toolbox/sap/goPtByAcf2.mdl Pitch scaling pitchShiftDemo/project1.exe pitchShift-multirate/multirate.m Intonation assessment ap170/matlab/goDemo.m