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4.1.3.Comparison

In this section, we explain the comparison of segments in order to get distances between segments that will be used in the Levenshtein distance measure. In a Barkfilter, the intensities of frequencies are given for a range of times. A spectrum contains the intensities of frequencies at one time. The smaller the time step, the more spectra there are in the acoustic representation. We consistently used the same time step for all samples.

It appears that the duration of the segment samples varies. This may be explained by variation in speech rate. Duration is also a sound-specific property. E.g., a plosive is shorter than a vowel. The result is that the number of spectra per segment may vary, although for each segment the same time step was used. Since we want to normalize the speech rate and regard segments as linguistic units, we made sure that two segments get the same number of spectra when they are compared to each other.

When comparing one segment of m spectra with another segment of n spectra, each of the m elements is duplicated n times, and each of the n elements is duplicated m times. So both segments get a length of m  n.

In order to find the distance between two sounds, the Euclidean distance is calculated between each pair of corresponding spectra, one from each of the sounds. Assume a spectrum e1 and e2 with n frequencies, then the Euclidean distance is:

E
quation 1. Euclidean distance

The distance between two segments is equal to the sum of the spectrum distances divided by the number of spectra. In this way we found that the greatest distance occurs between the [a] and ‘silence’. We regard this maximum distance as 100%. Other segment distances are divided by this maximum and multiplied by 100. This yields segment distances expressed in percentages. Word distances and distances between varieties which are based on them may also be given in terms of percentages.

In perception, small differences in pronunciation may play a relatively strong role in comparison with larger differences. Therefore we used logarithmic segment distances. The effect of using logarithmic distances is that small distances are weighed relatively more heavily than large distances. Since the logarithm of 0 is not defined, and the logarithm of 1 is 0, distances are increased by 1 before the logarithm is calculated. To obtain percentages, we calculate ln(distance + 1) / ln(maximum distance + 1).