Instantaneous RAPT algorithm
Abstract
This is the homepage of instantaneous RAPT (IRAPT) algorithm. It is a pitch estimation technique based on the robust algorithm for pitch tracking (RAPT) framework. IRAPT provides estimation of instantaneous pitch values and is not sensitive to rapid frequency modulations. The algorithm utilizes a different period candidate generating function based on instantaneous harmonic parameters. The function is similar to normalized crosscorrelation function, however it represents momentary periodicity with high frequency resolution. The second major revision of RAPT is an additional postprocessing procedure that makes estimation values more accurate. A short algorithm description
is given in
Azarov, E., Vashkevich, M. and Petrovsky, A., "Instantaneous pitch estimation based on RAPT framework" Proceedings of the 20th European Signal Processing Conference (EUSIPCO'2012), pp. 27872791, Bucharest, Romania, August 2731, 2012.
Matlab implementation of IRAPT algorithm can be found here .
You are welcome to send any questions, suggestions or error reports to the authors Elias Azarov azarov@bsuir.by and Maxim Vashkevich vashkevich.m@gmail.com.
Introduction
A pitch estimation technique based on the robust algorithm for pitch tracking (RAPT) framework [1]. The main features of the proposed algorithm are:
 estimation of instantaneous pitch;
 accurate processing of rapid pitch, modulations;
 high time/frequency resolution;
 low (quasilinear) computational complexity.
 period candidate generation function is calculated using instantaneous harmonic parameters;
 pitch values are recalculated in warped time domain.
Pitch estimation scheme
The pitch estimation scheme provides two pitch estimations: initial pitch estimation (denoted as "IRAPT 1") and recalculated pitch in time warped domain (denoted as "IRAPT 2").
Estimation of instantaneous harmonic parameters
The signal is decomposed into overlapping bandlimited analytical signals :
where  bandwidth and  center frequency of the ith band and  an even window function. Then instantaneous parameters are evaluated as
 amplitude
 frequency
 phase
Period candidate generating function
RAPT 
Normalized crosscorrelation function (NCCF) where and n  window size. 
IRAPT 
NCCF is calculated using instantaneous harmonic parameters where P is the number of bandlimited analytical signals. 
Time warping and pitch recalculation
Time warping eliminates pitch modulations. The signal is sampled with variable frequency aligned with estimated initial pitch contour. Resampling is carried out using sinc interpolation.
Pitch recalculation: new pitch values (denoted as "IRAPT 2" on the scheme) are calculated as:
Experimental results
The proposed technique is compared with other pitch estimation algorithms in terms of gross pitch error (GPE, %) and mean fine pitch error (MFPE, %).
Artificial signals
Natural speech

Male 
Female 

GPE 
MFPE 
GPE 
MFPE 

RAPT [1] 
3.69 
1.74 
6.07 
1.18 
YIN [2] 
3.18 
1.39 
3.96 
0.84 
SWIPE'[3] 
0.78 
1.51 
4.27 
0.80 
IRAPT 1 
1.63 
1.61 
3.78 
0.98 
IRAPT 2 
1.57 
1.57 
3.78 
1.05 
Conclusions
An instantaneous pitch estimation algorithm has been proposed. The algorithm has low sensitivity to rapid pitch modulations and provides accurate values with high time/frequency resolution. Due to its properties the algorithm can be useful in various applications such as speech analysis/synthesis and automatic rotational frequency tracking for mechanical devices.
Reference
[1] D. Talkin, "A Robust Algorithm for Pitch Tracking (RAPT)" in "Speech Coding & Synthesis", W B Kleijn, K K Paliwal eds, Elsevier ISBN 0444821694, 1995.
[2] A. Cheveigne and H. Kawahara "YIN, a fundamental frequency estimator for speech and music", Journal Acoust. Soc. Am., vol. 111, no. 4, pp 19171930, Apr. 2002.
[3] A. Camacho and J. G. Harris, "A sawtooth waveform inspired pitch estimator for speech and music", Journal Acoust. Soc. Am., vol. 123, no. 4, pp 16381652, Sep. 2008.