How to write code for f0 extraction in noise signal using autocorrelation

F0-ESTIMATION USING SHIFT-ACF

To estimate the time-varying F0 we first compute the shift- ACF for successive time frames of a speech signal y. For this,

we compute the spectrogram SG[y], where the j−th column

SG[y]:,j is obtained by computing the discrete Fourier trans- form of a suitably windowed version of the j-th time frame

(yjS, . . . , yjS+N−1) of length N extracted from y using step

size S. Then the spectral shift-ACF of type t is defined by

[y](s, j) := ACFt

computing the shift-ACF for each spectrogram column.

[SG[y]:,j ](s), i.e., by independently to start or end at each node. The resulting optimization prob-

Fig.3 shows the spectrogram (1) of a clean speech sig- nal (male speaker) of length 2.4 seconds taken from the Kiel

corpus [10]. For illustration, only frequencies up to 2 kHz

are shown. In the center (2), the type 100 spectral shift-ACF

is shown, where columns were postprocessed by normaliza- tion and thresholding by the median. The F0 is cleary visible

by sharp temporal trajectories between 130 and 190 Hz. For

comparison, (3) shows the type 0 spectral shift-ACF, corre- sponding to the classical ACF. Here, trajectories are more

blurred and significant energy is present at harmonic lags.

Now we extract significant time-varying F0 trajectories

from the spectral shift-ACF. First, a peak picking step is

performed. As F0 trajectories evolve in temporal direction,

this is done by successively considering each colum cj :=

SpACFt

[y]:,j . After thresholding cj by a smoothed, median-

filtered version, peaks are picked iteratively. Using a greedy

approach, in each step a maximum position is selected. In

subsequent iterations, the neigborhoods of already chosen po- sitions are ignored. In Fig. 4 (1), peaks extracted from a re- gion of our example in Fig. 3 (2) are shown as white circles.

For trajectory extraction we consider the set of m ex- tracted peaks as nodes in a graph. We then enforce paths

by connecting each node to exactly one successor node by

computing a bijection π : [1 : m] → [1 : m] such that the to- tal cost Pm

i=1 Ci,π(i) of connecting nodes is minimized. The

costs Ci,j of connecting node i to j are chosen to provide rea- sonable F0 trajectories: Ci,j is set to the Euclidean distance

between peaks i and j, where Ci,j := ∞ if peak i temporally

occurs after peak j. Furthermore, Ci,i := ∞ to prohibit 1-

cycles. By introducing additional dummy nodes at a suitable

maximum distance of each node, we furthermore allow a pathlem is a special case of a linear assignment problem (LAP)

which can be efficiently solved using, e.g., the algorithm pro- posed in [11]. A result of the path extraction for our running

example is shown in Fig. 4 (2).

Finally, paths which are too short or have only insignifi-

cant energy are discarded. For this, we use a trajectory sharp- ness measure such as in [1]. This measure, as illustrated

in Fig. 5, basically computes a logarithmic energy ratio be- tween an inner region Iτ around the estimated trajectory and

an outer region Oτ := O1

trajectories result in positive sharpness values. Fig. 5 shows

the sharpness measure evaluated for the finally resulting F0

trajectories in white color.

τ ∪ O2

. By construction, existing

τ