# Extraction of Vocal Tract Length from Formant Frequencies for Forensic Speech Applications in Noisy Environment

K. V. Aljinu Khadar, R. K. Sunil Kumar, V. V. Sameer

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K. V. Aljinu Khadar, R. K. Sunil Kumar, V. V. Sameer. Extraction of Vocal Tract Length from Formant Frequencies for Forensic Speech Applications in Noisy Environment. 6th International Conference on Computational Intelligence in Data Science (ICCIDS), Feb 2023, Chennai, India. pp.254-265, 10.1007/978-3-031-38296-3_20. hal-05466030

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# Extraction of Vocal Tract Length from Formant Frequencies for Forensic Speech Applications in Noisy Environment

K. V. Aljinu Khadar<fnref n="1" />(✉), R. K. Sunil Kumar<fnref n="1" />, and V. V. Sameer<fnref n="2" />

**Abstract.** In forensic speaker recognition, the speaker's vocal tract length (VTL) is an important factor. In this work formant frequency analysis of Malayalam vowels were carried out on sound samples collected from 100 speakers and their vocal tract lengths were found experimentally. We have estimated vocal tract length for five Malayalam vowel sounds for different speakers. Using formant frequencies, the effect of VTL on vowel production variation have been investigated here. Data were collected from 100 participants (52 females and 48 males) in five Malayalam vowels /a/, /e/, /u/, /ae/, and /o/. Each vowel was recorded ten times. The accuracy of the formant extraction technique is highly sensitive to the quality of the input sample. It works best with samples that don't have any noise, but its performance goes down when it's used with noisy data. The vocal tract was estimated using Pink Noise, White Gaussian Noise, and Red Noise with signal-to-noise ratios (SNRs) ranging from -20 dB to +20 dB. The autocorrelation-based formant extraction is a good way to find vocal tracts when there is a lot of noise in the background. This strategy improves the accuracy of VTL extraction even at extremely high noise levels (-20 dB) compared to previous research. This information is extremely valuable for forensic speaker recognition difficulties in environments with heavy background noise. The VTL can be employed for speaker normalization and parameter extraction.

**Keywords:** Vocal tract length · Forensic speaker recognition · static method · dynamic method

## 1 Introduction

Human communication is most naturally accomplished through speech. From the standpoint of speech production and perception, it conveys various types of information. The speech signal conveys linguistic information as well as the message [1]. The speech signal can also provide information about the speaker's emotional and physiological characteristics. It also provides information about the environment in which the speech

<footnote n="1">¹ Department of Information Technology, Kannur University, Kannur, India (aljinu,sunilkumarrk)@kannuruniv.ac.in</footnote>

<footnote n="2">² Department of Computer Science, Farook College, Kozhikode, India sameer@farookcollege.ac.in</footnote>
was created as well as the medium through which it was delivered [2]. As a result, a speech signal contains a large amount of information that is encoded in a complex manner. The majority of this data is easily decoded by humans. This has prompted researchers to create systems that automatically extract and process the vast amounts of information contained in speech, which can be extremely useful in forensic applications [3].

Forensics, often known as “forensic science,” refers to the application of scientific principles and technical methodologies to criminal investigations for the purposes of providing evidence of a crime’s occurrence, identifying its perpetrators, and understanding how the crime was committed [4]. It refers to the application of science or technology in a court of law to investigate and determine facts or evidence. A forensic practitioner is someone who uses evidence (whether objective or subjective) to assist authorities and courts in making decisions [5]. Forensic speaker recognition (FSR) is the process of finding out if a certain person (suspected speaker) is the origin of a speech recording that is being questioned (traced) [6]. This method compares recordings of a voice that is unknown (the “questioned recording”) to recordings of one or more voices that are known (the speech of the suspected speaker). Many methods are reported to extract formant frequency from speech signal. But formant frequency extraction from noisy speech signal is very challenging. The research goal is to analyse the speech signal in order to extract efficient parameters such as the speaker’s vocal tract length from fundamental frequencies in noisy environment for the development of a robust forensic speaker verification system.

## 2 Formant Frequency Analysis of Malayalam Vowels

Formant frequencies are the dominant frequencies of vocal tract resonance. In acoustics, it is usually described as a large peak or a local maximum in the spectrum. Formants are the frequencies that cause resonance at the glottis of the vocal tract filter. One problem with using formants is that different lengths of vocal tracts may make the same formant frequencies by changing the area function [7, 8].

A formant is an acoustic energy peaking at a certain frequency in a speech wave. Each formant occurs at a separate frequency; for normal men, there is one formant for every 1000 Hz [9]. The corresponding ranges for average women is one formant every 1100 Hz. The real range is based on how long the vocal tract is. Each formant is a mode of the vocal tract's resonance [10]. In a wideband spectrogram, formants appear as dark bands, as illustrated in the Fig. 1.

The $F_1$ is the lowest formant frequency, followed by the $F_2$, $F_3$ and $F4$ are the second, third and fourth formant frequencies respectively. $F_0$ is sometimes used to describe the fundamental frequency or pitch of the voice, but it is not a formant. Most of the time, only the first two formants, $F_1$ and $F_2$, are needed to figure out the vowels [11, 12], and all vowels have a “gap” between $F_1$ and $F_2$. The height of the tongue is inversely related to $F_1$, and both $F_2$ and $F_3$ are influenced by the degree of lip rounding. The values of the $F_1$ and $F_2$ frequencies are enough to tell vowel contrasts in most languages [13]. The actual formant frequencies will vary in value based on the speaker's head circumference and vocal tract length.

Many works are reported for the extraction of vocal tract length from speech signal [14–16]. The vocal tract length of a speaker is an important parameter for the extraction
<figure><img src="image_3.png" /><figcaption>Fig. 1. Spectrogram of vowel sound /a/ uttered by different times.</figcaption></figure>

speaker specific parameter like height and shape of the speaker [17–19]. In most of the forensic speaker verification cases background noise is a challenging problem [20]. So the application of noise robust methods in finding vocal tract length of the speaker is very essential in developing a robust speaker verification system.

# 3 Experiment Results

## 3.1 Data Base Creation

Speech signal band limited to 50–4000 Hz is sampled at 8 kHz rate and digitized using 16 bit A/D converter. We got information from about 100 participants, both men and women, who all grew up in Kerala and spoke Malayalam fluently, and used different kinds of mobile phones. Participants were recorded five Malayalam vowels /a/, /e/, /u/, /ea/ and /o/ and five Malayalam sentence. Each vowel recorded in ten times. The first four formants were extracted both statically and dynamically. Statistical analysis means feature extraction carried out at the entire portion of the speech waveform and dynamic means divide the speech wave into three equal parts and feature extraction is carryout. After analysis, the features from the three parts of the signal are averaged (Figs. 2, 3 and 4).

## 3.2 Formant Frequency Analysis by Noise Robust Method

When an additive noisy signal $c(p, q)$ corrupts a speech signal $s(p, q)$, the affected speech signal is denoted as

$$b(p, q) = [s(p, q) + c(p, q)], \quad 0 \le p \le M-1 \quad 0 \le q \le N-1 \quad (1)$$

The expression for the autocorrelation function of the noisy voice signal $b(p)$ is:

$$r_{bb}(p, k) = r_{ss}(p, k) + r_{cc}(p, k), \quad 0 \le p \le M-1 \quad 0 \le k \le N-1 \quad (2)$$

One-sided autocorrelation sequences for noisy speech, clean speech, and noise are $r_{bb}(p, k)$, $r_{ss}(p, k)$ and $r_{cc}(p, k)$, where k is the index of the autocorrelation sequence
<figure><img src="image_4.png" /><figcaption>Fig. 2. Static Method</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Dynamic Method.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Box plots of formant frequencies of some vowel sound of female speaker both in static and dynamic method.</figcaption></figure>
inside each frame [21–23]. Autocorrelation is a better way to represent speech signals that are noisy so that the information from the source can be taken out. Most of the noisy signal’s coefficient of autocorrelation is close to the smaller lag, while those close to the larger lag are very small. Taking out the lower-order autocorrelation coefficients of a noisy speech signal will get rid of the main noise sources [24]. The sequence of speech that has already been auto-correlated is then put through formant frequency extraction. This method is very helpful for analyzing the speaker in a noisy environment for forensic purposes [25].

## 3.3 Vocal Tract Length (VTL) and Formant Frequency Analysis

Modern speech processing requires an accurate estimation of the VTL. In theory, it should be feasible to accurately estimate the VTL from acoustic information alone [26]. There are numerous practical applications for a system that can estimate the VTL from speech signal [27].

Formant frequencies are resonances of an open tube with an open end (the mouth) and a closed end (the glottis) [28]. By applying the physics of open tube resonance we can estimate the length of the vocal tract tube. In real scenario vocal tract is a multi tube with varying areas of cross sections. But in this work we treated it as uniform open tube. In this modeling the VTL and formant frequencies are related (Fig. 5).

<figure><img src="image_7.png" /><figcaption>Fig. 5. Uniform Tube Model</figcaption></figure>

By Eq. (3) where L is the VTL, c is the velocity of sound and $\Phi$ is first resonant frequency [7].

$$L = \frac{c}{4\Phi} \qquad (3)$$

For uniform lossless tube model $\Phi$ and formant frequencies are related as

$$F_n = \Phi(2n - 1) \quad n = 1, 2, 3 \dots \qquad (4)$$

Fitch [17] developed a measure he named “Frequency Dispersion” that takes into account the average separation of every pair of formants:

$$\hat{\Phi}_{FD} = \frac{F_2 - F_1}{2(m-1)} + \frac{F_3 - F_2}{2(m-1)} + \dots + \frac{F_m - F_{m-1}}{2(m-1)} \qquad (5)$$
Since many of the components in Eq. (5) finally cancel out, it can be greatly simplified. Eventually, the equation can be rewritten as

$$ \hat{\Phi}_{FD} = -\frac{F_1}{2(m-1)} + \frac{F_m}{2(m-1)} \quad (6) $$

We calculated the VTL using two methods method1 (M1) and method2 (M2) by using the Eqs. (4) and (6) (Fig. 6).

<figure><img src="image_8.png" /><figcaption>Fig. 6. Architectural Diagram for vocal tract extraction</figcaption></figure>

In this work, the first step in VTL estimation is the pre-processed speech signal is corrupted by adding different types of noise like whit noise, pink noise and red noise in different signal to noise ratios. This noise corrupted signal is then transformed into the autocorrelation domain for noise removal. The four formant frequencies extracted by both static and dynamics methods. The vocal tract lengths are extracted for each vowels uttered by both male and female speakers. The VTLS are also calculated using two different values specified by Eqs. (4) and (6). These are denoted as VTL (M1) and VTL (M2).

Table 1 and Fig. 7 shows the vocal tract length of a given speaker for all five vowels of Malayalam using static method for female speaker and its variations for female speaker.

<table><caption>Table 1. Vocal Tract Length of Female Speaker in Static Method</caption><thead><tr><td>Vowel</td><td>VTL (M1) in cm</td><td>VTL (M2) in cm</td></tr></thead><tbody><tr><td>/a/</td><td>18.45</td><td>23.29</td></tr><tr><td>/e/</td><td>18.61</td><td>18.99</td></tr><tr><td>/u/</td><td>22.16</td><td>20.16</td></tr><tr><td>/ae/</td><td>18.02</td><td>20.35</td></tr><tr><td>/o/</td><td>21.77</td><td>20.26</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Vocal tract length variation for each vowel in static method for female speakers (Color figure online)</figcaption></figure>

Blue, Green, Red, Yellow and Black are Vocal tract length of sounds /a/, /e/, /u/, /ae/ and /o/ respectively.

From the Fig. 7, we can see that in female, vocal tract length of vowel /e/ is higher than that of other vowels. And vocal tract length of vowel /ae/ has shorter vocal tract length.

Table 2 and Fig. 8 shows the vocal tract length of a given speaker for all five vowels of Malayalam using static method for male speaker and its variations for female speaker.

<table><caption>**Table 2.** Vocal Tract Length of Male Speaker in static Method</caption><thead><tr><td>Vowel</td><td>VTL (M1) in cm</td><td>VTL (M2) in cm</td></tr></thead><tbody><tr><td>/a/</td><td>18.74</td><td>24.61</td></tr><tr><td>/e/</td><td>19.29</td><td>17.17</td></tr><tr><td>/u/</td><td>22.88</td><td>19.08</td></tr><tr><td>/ae/</td><td>18.85</td><td>20.79</td></tr><tr><td>/o/</td><td>21.08</td><td>18.86</td></tr></tbody></table>

Blue, Green, Red, Yellow and Black are Vocal tract length of sounds /a/, /e/, /u/, /ae/ and /o/ respectively.

From the above plot we can see that in male, vocal tract length of vowel /e/ is higher than that of other vowel sounds. And vocal tract length of vowel /ae/, /a/ and /u/ has shorter vocal tract length.

Table 3 and Fig. 9 shows the vocal tract length of a given speaker for all five vowels of Malayalam using dynamic method for female speaker and its variations for female speaker.

Blue, Green, Red, Yellow and Black are vocal tract length of sounds /a/, /e/, /u/, /ae/ and /o/ respectively.
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Vocal tract length variation for each vowel in static method for male speakers (Color figure online)</figcaption></figure>

<table><caption>**Table 3.** Vocal Tract Length of Female Speaker in Dynamic Method</caption><thead><tr><td>Vowel</td><td>VTL (M1) in cm</td><td>VTL (M2) in cm</td></tr></thead><tbody><tr><td>/a/</td><td>17.58</td><td>23.82</td></tr><tr><td>/e/</td><td>18.22</td><td>19.10</td></tr><tr><td>/u/</td><td>22.02</td><td>20.23</td></tr><tr><td>/ae/</td><td>17.90</td><td>20.33</td></tr><tr><td>/o/</td><td>21.74</td><td>20.28</td></tr></tbody></table>

From the above graph, we can see that the vowel sound /e/ has a higher VTL in females than other vowel sounds. The VTL for the vowel /ae/ is shorter.

Table 4 and Fig. 10 shows the VTL of a given speaker for all five vowels of Malayalam using dynamic method for male speaker and its variations for female speaker.

Blue, Green, Red, Yellow and Black are Vocal tract length of sounds /a/, /e/, /u/, /ae/ and /o/ respectively.

From the above plot we can see that in male, vocal tract length of vowel /e/ is higher than that of other vowel sounds. And vocal tract length of vowel /ae/ and /a/ has shorter VTL and variation of VTL for each vowel is in the same order for different speakers.

For the vocal tract estimation experiment, Pink Noise, White Gaussian Noise, and Red Noise with SNR values from -20 dB to +20 dB were added. Autocorrelation-based formant extraction is an effective technique for locating the vocal tract in the presence of severe background noise [29]. This strategy improves the accuracy of VTL extraction even at extremely high noise levels (-20 dB) compared to previous research. Figure shows the percentage of error in estimation of vocal tract length for auto-correlated speech signal which is corrupted by adding noise (Fig. 11).

The VTL information can be used for identifying speaker specific features.
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Vocal tract length variation for each vowel in dynamic method for female speakers (Color figure online)</figcaption></figure>

<table><caption>**Table 4.** Vocal Tract Length Estimation of Male Speaker in Dynamic Method</caption><thead><tr><td>Vowel</td><td>VTL (M1) in cm</td><td>VTL (M2) in cm</td></tr></thead><tbody><tr><td>/a/</td><td>17.84</td><td>24.86</td></tr><tr><td>/e/</td><td>19.59</td><td>17.16</td></tr><tr><td>/u/</td><td>22.90</td><td>19.07</td></tr><tr><td>/ae/</td><td>19.34</td><td>20.92</td></tr><tr><td>/o/</td><td>21.03</td><td>18.75</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Vocal tract length variation for each vowel in dynamic method for male speakers. (Color figure online)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Percentage of error in estimation of the length of vocal tract</figcaption></figure>

## 4 Conclusion

Vocal tract length of the speaker is an important attribute in Forensic speaker recognition. In this work formant frequency analysis of Malayalam vowels were carried out on sound samples collected from 100 speakers and their vocal tract lengths were found out experimentally. We have estimated the VTL for five Malayalam vowel sounds for different speaker. Here role of VTL in vowel production variability has been studied using formant frequencies. Data were collected from 100 participants (52 female, 48 male). They were recorded five Malayalam vowels /a/, /e/, /u/, /ae/ and /o/. Each vowel was recorded 10 times. The formant extraction process is highly dependent on sample quality. It yields optimal results with noiseless samples but degrades when used to noisy data. Experiments on the estimate of the vocal tract have been undertaken using Pink
Noise, White Gaussian Noise, and Red Noise with SNR values ranging from -20 to +20 dB. The autocorrelation-based formant extraction is a good way to find the vocal tract when there is a lot of noise in the background. The accuracy of VTL extraction is better with this method, even when there is a lot of noise (-20 dB) around. This information is extremely useful for solving the challenge of forensic speaker recognition in environments with significant background noise. The VTL can be utilised to determine speaker-specific characteristics.

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