As soon as the closing instant has been determined, the same has to be done with respect to the opening instant. As stated further above, it is usually assumed that at the opening the descent of the EGG waveform becomes rapid, producing a knee in the curve (Childers & Krishnamuthy, 1985; Baer et al., 1983). This instant corresponds to the minimum of the waveform time derivative as depicted in Fig 18. Without question, this can be used to evaluate the EGG duty cycle:
using the notation given in Fig.22:
This quantity is defined equally to the Open Quotient of the glottal flow (as defined in section 7.1) provided that assumption that the opening instant is determined correctly. Numerous researchers (Childers & Lee, 1991; Childers & Ahn, 1995; Childers & Wong , 1994;Koreman, 1996) use this estimate as a reliable indication of glottal opening. This instant is often used for the determination of the closed glottis phase in simultaneous recordings of speech and EGG signals and allows a precise estimation of the vocal tract transfer function which is necessary for inverse filtering. The validity of the measurement of the glottal opening in the EGG signal is doubtful due to the mucus bridging effect (as described in section 9). Also Baer et al. (1983) report that in a simultaneous observation of EGG, PGG and high-speed filming, it was found that the opening can be gradual and that no knee in the EGG waveform was observed for the steady phonation of a female speaker (with no evidence of laryngeal pathology). In their experiment the closure instant i was easily distinguishable in the EGG signal. "The EGG signal is also consistent with the notion that glottal opening is more gradual in both the vertical and horizontal dimensions. For the female subject, glottal opening cannot be clearly identified in the EGG waveform; for the male subject, it corresponds only to a mild increase in the rate-of-fall of the curve" (Baer et al. ,1983:1307). Indeed, in our experiments the waveforms without the knee in the opening phase were much more frequent then those with one. Baken (1992:108) quotes the recommendation of the Voice Committee of the IALP: "[..] numerical measures (e.g. open quotient) that depend on open and closed times derived form electroglottograms must be considered to be of questionable validity. Their use is not recommended".
However, a slight redefinition of the Open Quotient can validate a new measure which constitutes a more accurate and reliable estimation of the glottal duty cycle. After careful examination of the EGG phenomena Rothenberg and Mahshie (1988) have developed a criterion which utilizes the amplitude variations of the Lx signal. They used the 35% threshold of the peak EGG amplitude to get to an estimate of the open phase duration in the EGG period. Such an estimate can be obtained by registering the instant at which the EGG waveform crosses a given criterion level. Before this procedure the waveform must have been filtered (highpass), so that the low frequency noise and the artifacts of electrode movement are removed. Rothenberg and Mahshie (1988) conclude that the criterion produces consistent duty cycles in normal, breathy and tightly adducted voices. In their investigation they examined the 35% and 50% threshold levels and the area-equalization criterion (the area between the waveform and below/above the criterion line are equal). The 35% criterion is advantageous especially for breathy voices. This problem was also addressed by Davis et al. (1986). In that investigation the authors compared three different ways of defining the opening instant for the Lx component of the EGG (without Gx influence):
1. the opening corresponds to a position where Lx has reached a value that divides the range of the peak-to-peak amplitude to a fixed 7:3 ratio (ratio of the peak value of Lx to the value at the opening instant)
2. the opening coincides with the maximum positive derivative of Lx - the "knee" in the Lx waveform
3. the opening occurs when the Lx signal has the same value it had in the previous closure
The results are compared using the following data:
They come to the conclusion that all three methods of calculating the position of glottal opening exhibit consistent results; the third method produces slightly shorter closed phases. There is also a subtle suggestion that the first method performs better than the others. Orlikoff (1991) also used the threshold criterion for examining the instant of opening. The threshold was set at a level of 25% level of the peak-to-peak amplitude. The results obtained for modal speakers comprized the relations already known from other investigations, relating the OQ to speech loudness, which (indirectly) validates the EGG results. A method similar to the third one of those listed above was utilized by Dejonckere and Lebacq (1985) in the examination of the influence of vocal nodules on the EGG waveform. They compared the waveform areas above and below half of the peak-to-peak amplitude. Comparing 25 normal and 22 pathological subjects they found a significant difference using this characteristic (no pathological subject reach the mean value of the quotient for the normal subjects).
The Open Quotient determined in the EGG waveform is used by Rothenberg and Mahshie (1988) to characterize vocal fold abduction. They introduce an index (AbQ) with values ranging from 0 (complete closure of the vocal folds, i.e. complete adduction) to 1 (total opening, i.e.complete abduction). On the basis of a simplified model of vocal fold movement they derive the vocal folds abduction quotient from the Open Quotient:
Summarising it has to be stated that the legitimacy of the use of the EGG-based Open Quotient is questionable, mainly due to problems concering the determination of the glottal opening instant. The identification of this instant may be additionally biased because of the EGG baseline drift as well as because of phenomena which distort the electrical current flow (e.g. mucus bridging effect). Instead, measures related to the Open Quotient were introduced which do not provide an exact estimation of the duty cycle, but a value which depends on it.
Since the EGG allows for a better representation of the closed phase of the vocal fold movement, a complementary measure, the Close Quotient (CQ), has also been introduced (Houben et al., 1992). However, determination of the opening instant is still required6.
6 the closed phase duration is sometimes estimated at the value of 30% of each peak EGG amplitude (Fourcin, 1997)