Auto-correlation (autocorrelationProc.m)¶

Auto-correlation is an important computational concept that has been extensively studied in the context of predicting human pitch perception [Licklider1951], [Meddis1991]. To measure the amount of periodicity that is present in individual frequency channels, the ACF is computed in the FFT domain for short time frames based on the IHC representation. The unbiased ACF scaling is used to account for the fact that fewer terms contribute to the ACF at longer time lags. The resulting ACF is normalised by the ACF at lag zero to ensure values between minus one and one. The window size ac_wSizeSec determines how well low-frequency pitch signals can be reliably estimated and common choices are within the range of 10 milliseconds – 30 milliseconds.

For the purpose of pitch estimation, it has been suggested to modify the signal prior to correlation analysis in order to reduce the influence of the formant structure on the resulting ACF [Rabiner1977]. This pre-processing can be activated by the flag ac_bCenterClip and the following nonlinear operations can be selected for ac_ccMethod: centre clip and compress ’clc’, centre clip ’cc’, and combined centre and peak clip ’sgn’. The percentage of centre clipping is controlled by the flag ac_ccAlpha, which sets the clipping level to a fixed percentage of the frame-based maximum signal level.

A generalised ACF has been suggested by [Tolonen2000], where the exponent ac\_K can be used to control the amount of compression that is applied to the ACF. The conventional ACF function is computed using a value of ac\_K=2, whereas the function is compressed when a smaller value than 2 is used. The choice of this parameter is a trade-off between sharpening the peaks in the resulting ACF function and amplifying the noise floor. A value of ac\_K = 2/3 has been suggested as a good compromise [Tolonen2000]. A list of all ACF-related parameters is given in Table 23. Note that these parameters will influence the pitch processor, which is described in Pitch (pitchProc.m).

Table 23 List of parameters related to the auditory representation 'autocorrelation'.
Parameter Default Description
ac_wname 'hann' Window type
ac_wSizeSec 0.02 Window duration in s
ac_hSizeSec 0.01 Window step size in s
ac_bCenterClip false Activate centre clipping
ac_clipMethod 'clp' Centre clipping method 'clc', 'clp', or 'sgn'
ac_clipAlpha 0.6 Centre clipping threshold within [0,1]
ac_K 2 Exponent in ACF

A demonstration of the ACF processor is shown in Fig. 26, which has been produced by the scrip DEMO_ACF.m. It shows the IHC output in response to a 20 ms speech signal for 16 frequency channels (left panel). The corresponding ACF is presented in the upper right panel, whereas the SACF is shown in the bottom right panel. Prominent peaks in the SACF indicate lag periods which correspond to integer multiples of the fundamental frequency of the analysed speech signal. This relationship is exploited by the pitch processor, which is described in Pitch (pitchProc.m).

 [Licklider1951] Licklider, J. C. R. (1951), “A duplex theory of pitch perception,” Experientia (4), pp. 128–134.
 [Meddis1991] Meddis, R. and Hewitt, M. J. (1991), “Virtual pitch and phase sensitivity of a computer model of the auditory periphery. I: Pitch identification,” Journal of the Acoustical Society of America 89(6), pp. 2866–2882.
 [Rabiner1977] Rabiner, L. R. (1977), “On the use of autocorrelation analysis for pitch detection,” IEEE Transactions on Audio, Speech, and Language Processing 25(1), pp. 24–33.
 [Tolonen2000] (1, 2) Tolonen, T. and Karjalainen, M. (2000), “A computationally efficient multipitch analysis model,” IEEE Transactions on Audio, Speech, and Language Processing 8(6), pp. 708–716.