Complexity-based decoding of the relation between human voice and brain activity

Abstract

BACKGROUND:

The human voice is the main feature of human communication. It is known that the brain controls the human voice. Therefore, there should be a relation between the characteristics of voice and brain activity.

OBJECTIVE:

In this research, electroencephalography (EEG) as the feature of brain activity and voice signals were simultaneously analyzed.

METHOD:

For this purpose, we changed the activity of the human brain by applying different odours and simultaneously recorded their voices and EEG signals while they read a text. For the analysis, we used the fractal theory that deals with the complexity of objects. The fractal dimension of EEG signal versus voice signal in different levels of brain activity were computed and analyzed.

RESULTS:

The results indicate that the activity of human voice is related to brain activity, where the variations of the complexity of EEG signal are linked to the variations of the complexity of voice signal. In addition, the EEG and voice signal complexities are related to the molecular complexity of applied odours.

CONCLUSION:

The employed method of analysis in this research can be widely applied to other physiological signals in order to relate the activities of different organs of human such as the heart to the activity of his brain.

Keywords

Human voice brain electroencephalography (EEG) signal odours fractal dimension complexity

1. Introduction

The brain is the main processing unit of the human body. It controls all actions/reactions of the human by sending impulses to different parts of the body. The voice is the main feature of communication for humans and its analysis is therefore of great importance. It is known that the human brain processes the voice.

For years, many works have investigated the activity of the human brain in different conditions. The major part of these studies analyzed how the human brain reacts to external stimuli. The works that studied the effect of visual [1, 2], auditory [3, 4], somatosensory [5], touch [6], and olfactory [7] stimuli on the human brain are worth mentioning. On the other hand, some scientists worked on the analysis of human voice, i.e. speech. The are several studies that investigated the effect of stress on human speech [8, 9], worked on the modelling of speech under different conditions [10], detected the effect of human’s emotional state on his voice [11], and performed statistical analysis on human speech sounds to predict musical universals [12].

Besides the reported works on the analysis of the activity of the brain or voice, no study investigated the relationship between brain and voice activity. Therefore, in this research, we investigated the relationship between human voice and brain activity. We aimed to make a link between voice and brain activities from a mathematical point of view. For this purpose, since EEG signal, as the feature of brain activity, and voice signal are random signals that have complex structures, we used fractal theory for the analysis. The fractal theory is a fast-growing mathematical technique that is used to define the complexity of self-similar or self-affine objects [13].

Through the years, researchers employed fractal analysis to analyze different time series and images in different areas of science and engineering. By focusing on the application of fractal theory in biomedical engineering, heart rate [14], eye movement [15, 16, 17, 18], electromyography signal (EMG) [19, 20, 21, 22, 23], magnetoencephalography (MEG) [24], face and DNA [25, 26, 27], respiration [28], s-ABR signal [29, 30], and Galvanic Skin Response (GSR) signal [31] are investigated by applying fractal analysis. Similarly, many studies employed the fractal theory to analyze human EEG signal in different conditions. The reported works that analyzed the effect of visual [32, 33] and auditory stimuli [34, 35], aging [36, 37], brain diseases [38, 39, 40] and body movements [41, 42, 43] on variations of EEG signal using fractal theory, are worth mentioning. However, the application of fractal theory in voice (i.e. speech) processing is very limited. The studies that applied fractal analysis for speech segmentation and phonetic classification [44], modelling of speech signals [45], prediction in waveform coding of speech signals [46], detection of voice disorder in patients [47, 48] and classification of speech [49] are worth mentioning.

Therefore, in this research, we used fractal theory to link the characteristic of voice to the characteristic of the brain activity by analyzing voice and EEG signals.

The rest of the paper is structured as follows: in the second section, the method of analysis based on fractal theory is presented. In the third section, the details of data collection procedure and analysis are provided. In the fourth section, the obtained results from the analysis is provided. In the fifth section, the obtained results and some future works are discussed.

2. Method

In this paper, we aimed to analyze the relationship between the complexity of human brain signal (EEG signal) and voice signal in different conditions. The applied conditions were the smells that were generated by fruit flavours (pineapple, banana, vanilla and lemon flavours) to stimulate subjects. For this purpose, we changed the activity of the human brain by applying different odours and analyzed whether human brain and voice signals are related when subjects read a text. Since EEG and voice signals are complex, fractal theory is employed to analyze their self-affine structures [50]. The fractal dimension is considered as the measure of the complexity of EEG and voice signals.

In general, fractal dimension can be computed using different methods that are mainly based on the entropy concept [51]. For a time series, the fractal dimension can have a value between 0 and 2. The greater value indicates a greater level of complexity [52]. The box counting method is the most famous method for computing the fractal dimension of objects. In this method, the object (i.e. signal in this research) is covered with a series of boxes in different steps, where the size of boxes is the same in each step. In each step, the algorithm counts the number of boxes that were used to completely cover the object [53]. After the algorithm repeated this procedure for different box sizes, the fractal dimension of an object is calculated based on the regression line that was fitted to log-log plot of a number of boxes ( $N$ ) versus scale ( $\varepsilon$ ) [54]:

$\displaystyle{FD}=\lim_{\varepsilon\to 0}\frac{\log N(\varepsilon)}{\log 1/\varepsilon}$ (1)

The fractal dimension of order $c$ can be formulated as [55]:

$\displaystyle{FD}_{c}=\lim_{\varepsilon\to 0}\frac{1}{c-1}\frac{\log\sum% \nolimits_{j=1}^{N}{r_{j}^{c}}}{\log\varepsilon}$ (2)

where $r_{j}$ is named as the probability of a number of occurrences that is defined as:

$\displaystyle r_{j}=\lim_{T\to\infty}\frac{t_{j}}{T}$ (3)

where $t_{j}$ and $T$ represent the total time of occurrence in the j-th bin and the total time span of the time series respectively.

We are interested in relating the human voice to the applied odours. In order to do this, we considered the complexity of odours by defining their molecular complexity. For our experiment, we chose four pleasant odours as olfactory stimuli and selected odours based on their molecular complexities. Bertz Formula (Eq. (1)) is applied for the calculation of molecular complexity that composes of two terms. The first term ( $C_{n}$ ) measures the skeletal complexity as a function of bond connectivity ( $\eta$ ), and the second term ( $C_{e}$ ) is a function of the diversity of the atoms in the molecule [56]. It is known that small and/or highly symmetrical molecules and compounds with few distinct atom types (or elements) have low complexity.

$\displaystyle C=C_{n}+C_{e}$ (4)

Figure 1 shows the molecular structure of selected odours. The first four selected odours include pineapple, banana, vanilla and lemon flavour, which all have increasing molecular complexities (see Table 1). As mentioned above, the odours were selected based on their complexities, which enabled us to investigate the relationship between the complexities of EEG signal, voice signal and odours.

Figure 1.

The molecular structure of different odours (stimuli).

Table 1

The chemical formula and molecular complexity of different odours (stimuli)

Odour	Chemical formula	Molecular complexity
Pineapple flavour	C6H12O2	68.9
Banana flavour	C7H14O2	86.9
Vanilla flavour	C8H8O3	135
Lemon flavour	C10H16	163

In different steps of the experiment, subjects were stimulated using different odours and then the relationship between the complexity of the voice signal and the complexity of the EEG signal were analyzed. The obtained result on fractal analysis of EEG and voice signals is discussed in relation to the variations of the molecular complexity of odours.

3. Data collection and analysis

All procedures of recruiting subjects and conducting the experiment were approved by the Monash University Human Research Ethics Committee (MUHREC) under ethical number 18260. The study was carried out in accordance with the approved guidelines.

The experiment was conducted on ten healthy students (18–22 years old) from Monash University, Malaysia. We screened the subjects about their health conditions and drinking alcohol/coffee (within 48 hours prior the experiment). The screening was in the form of questions. All participants signed an informed consent form prior to the experiment.

The experiment was conducted in a quiet room in order to isolate subjects from unwanted stimuli that could affect the recorded EEG and voice signals. In the experiment, subjects were seated comfortably in front of the computer monitor. Subjects were instructed to sniff the odours and read the text from the monitor of a computer in front of them.

The collection of EEG signals was done using Muse headband with the sampling frequency of 256 Hz. It should be noted that the voice recording app on the mobile phone was applied to record the voice of subjects. For stimulation of subjects, 0.01 ml of each flavour (Fig. 2) was spilt on a small piece of paper and kept near the nose of the subjects and were then asked to sniff it while reading the text.

First, EEG and voice signals were recorded while subjects read the text from the computer monitor without sniffing an odour. Second, the subjects rested for one minute without receiving any external stimuli. Then, subjects sniffed the first odour while reading the same text, and their EEG and voice signals were recorded. After that, the subjects rested for one minute while sniffing coffee. This procedure was continued to collect EEG and voice signals from subjects in case of second, third and fourth odours, with one minute of rest between stimulations. The data collection was repeated in the second session to consider the repeatability of data.

Figure 2.

Olfactory stimuli (fruit flavours).

Since subjects only received olfactory stimuli, the olfactory bulb of the brain was mainly stimulated and therefore only the recorded data from AF7 and AF8 channels was analyzed, as these are the closest electrodes to the olfactory bulb of the brain.

The raw EEG data was pre-processed to remove noises. For this purpose, a set of codes in MATLAB based on Butterworth filter with the frequency band of 0.5–30 Hz were written. It should be noted that due to the high sampling frequency of the recorded voice, we performed down-sampling on the voice data. For this purpose, we took a value between every 10 values. Then, we proceeded with the calculation of the fractal dimension of EEG and voice signals in MATLAB using the box counting method.

After computation of the fractal dimension for EEG and voice signals, statistical analysis had been performed on the obtained results. The effect of different stimuli on the variations of the fractal dimension of EEG and voice signals using effect size analysis was analyzed. Also, the significance of the difference between the fractal dimension of different pairs of data using posthoc Tukey test was analyzed. A significance level of 95% was considered in case of both statistical analyses.

4. Results

In this section, the result of our analysis is presented. It should be noted that out of one hundred sets of data that were collected from the ten subjects, four sets of data did not fall within the proper range and were therefore excluded from the analysis.

Figure 3 shows the mean value of the variations of the fractal dimension of the EEG signal (a) and the molecular complexity of odours (b).

Figure 3.

The fractal dimension of EEG signal and the molecular complexity of odours.

As can be seen in Fig. 3, the EEG signal has the lowest fractal dimension in case of no-odour condition. After that, the fractal dimension of the EEG signal increases when there is a move from the first odour to the fourth odour. Since fractal dimension indicates the complexity of the object, it can be concluded that the complexity of EEG signal increases with the increment of the molecular complexity of odours.

The results of effect size analysis are listed in Table 2, which indicate that the fourth odour had the greatest effect on the complexity of the EEG signal. The result of the posthoc Tukey test is also listed in Table 2. As can be seen from this table, there is no significant difference in the fractal dimension of the EEG signal between different pairs of conditions. Here, it should be noted that, to make the experiment relaxing for subjects, only a limited amount (0.01 ml) of odour was applied. Therefore, increasing the amount of odour could lead to a significant difference in the fractal dimension of the EEG signal.

Table 2

$p$ -value and effect size (r) in case of comparison of fractal dimension of EEG signal between different conditions

Comparison	$p$ -value	Effect size (r)
No stimulus vs. first odour	0.9825	0.0811
No stimulus vs. second odour	0.9585	0.1135
No stimulus vs. third odour	0.9381	0.1158
No stimulus vs. fourth odour	0.8703	0.1628
First odour vs. second odour	0.9999	0.0203
First odour vs. third odour	0.9995	0.0316
First odour vs. fourth odour	0.9944	0.0659
Second odour vs. third odour	1.0000	0.0148
Second odour vs. fourth odour	0.9985	0.0529
Third odour vs. fourth odour	0.9997	0.0315

Table 3

$p$ -value and effect size (r) in case of comparison of fractal dimension of voice signal between different conditions

Comparison	$p$ -value	Effect size (r)
No stimulus vs. first odour	0.9854	0.0950
No stimulus vs. second odour	0.9306	0.1317
No stimulus vs. third odour	0.9169	0.1484
No stimulus vs. fourth odour	0.4867	0.2118
First odour vs. second odour	0.9990	0.0493
First odour vs. third odour	0.9980	0.0637
First odour vs. fourth odour	0.8215	0.1547
Second odour vs. third odour	1.0000	0.0099
Second odour vs. fourth odour	0.9188	0.1128
Third odour vs. fourth odour	0.9380	0.1094

Figure 4.

The fractal dimension of the voice signal.

Figure 4 shows the variations of the fractal dimension of the voice signal. As can be seen in this figure, the voice signal has the greatest fractal dimension in case of no-odour condition. After that, the fractal dimension of voice signal decreases when there is a move from the first to the fourth odour. As mentioned before, fractal dimension indicates the complexity of the object, and it can therefore be said that the complexity of the voice signal decreases with the increment of the molecular complexity of odours (Fig. 3b). The effect size results (Table 3) indicate that the fourth odour had the greatest effect on the complexity of voice signal. However, the result of posthoc Tukey test in Table 3 indicates that there was no significant difference in the fractal dimension of the voice signal between different pairs of conditions. As mentioned before, presenting a greater volume of odours could lead to a significant effect on variations of the complexity of voice signal.

Comparing the obtained results in Fig. 4 with the variations of fractal dimension of EEG signal in Fig. 3a indicates that the variations of the complexity of voice signal are linked to the variations of the complexity of EEG signal.

Based on the obtained results, it can be said that since the brain controls the human voice, the variations in the complexity of human voice are related to the variations in the complexity of the brain signal.

5. Discussion

In this paper, for the first time the relationship between human voice and brain (EEG) signals was analyzed in different conditions. The applied conditions include the application of different pleasant odours (using fruit flavours). Based on the obtained results, the fractal dimension of the EEG signal increases with the increment of the molecular complexity of applied odours. Similarly, the fractal dimension of the voice signal experiences greater changes with the increment of the molecular complexity of applied odours. Since fractal dimension stands for complexity, it can be said that the variations in the complexity of voice signals are related to the variations in the complexity of EEG signals as well as the molecular complexity of odours. Statistical analysis also confirmed the obtained results, where the fourth stimulus with the greatest complexity had the greatest effect on the complexity of EEG and voice signals. In addition, the obtained results showed the greater variations in the complexity of the EEG signal compared to the variations of the complexity of the voice signal.

Even though the obtained results from the posthoc Tukey test indicat an insignificant difference in the variations of the complexity of EEG and voice signals between different conditions, this result could be significant if we apply a greater amount of odours. Therefore, the variations in the complexity of the voice signal which are coupled with the variations in the complexity of the EEG signal have been successfully shown. In fact, this study is one step forward compared to the studies that only analyzed the variations of EEG or voice signals in different conditions without relating voice to brain activity.

The obtained results in this study can be elaborated by the mechanism of speech. As mentioned before, the human voice is controlled by the brain. On the other hand, different stimuli (i.e. odours in this research) change the level of brain activity. Therefore, when the level of brain activity changes, the level of voice complexity will change as well.

It should be noted that the analysis in this research can be expanded in case of subjects with speech problems in order to decode the relation between their voice and brain activities by fractal analysis of voice and EEG signals. Finding the relation between brain and voice activities in case of these patients can help physicians with finding better treatments.

The method of analysis in this research can be widely employed in order to analyze the relationship between different physiological signals and the brain activity in order to study the relationship between different organs of the human body and the brain activity. For instance, since the human heart is controlled by the brain, we can analyze the relationship between the complexity of heart rate and EEG signal in different conditions. In another example, since human eye movement is controlled by the brain, we can investigate how eye movement is linked to the brain activity by analysis of the complexity of eye movement versus EEG signal.

In another category of work, researchers can potentially generate a mathematical model between external stimuli, EEG signal and human voice (or other physiological signals). This model should be able to predict the complexity of the human voice based on the stimulus and EEG signal. For this purpose, different mathematical models [57, 58, 59] would be helpful, in particular fractional diffusion models [60]. Overall, these attempts can help scientists to understand how the human brain controls different parts of the human body.

Footnotes

Conflict of interest

None to report.

References

Kim

J.Y.

Kim

S.Y.

The effects of visual stimuli on EEG mu rhythms in healthy adults. J. Phys. Ther. Sci. 28(6) (2016), 1748–1752.

O’Sullivan

J.A.

Crosse

M.J.

Power

A.J.

Lalor

E.C.

The effects of attention and visual input on the representation of natural speech in EEG. Conf Proc IEEE Eng. Med. Biol. Soc. 2013, pp. 2800–3.

Namazi

, et al. Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal. Oncotarget. 7 (2016), 56120–56128. doi: 10.18632/oncotarget.11234.

Kučikienė

Praninskienė

The impact of music on the bioelectrical oscillations of the brain. Acta Med. Litu. 25(2) (2018), 101–106.

Kattler

Dijk

D.J.

Borbély

A.A.

Effect of unilateral somatosensory stimulation prior to sleep on the sleep EEG in humans. J. Sleep Res. 3(3) (1994), 159–164.

Singh

, et al. The brain’s response to pleasant touch: An EEG investigation of tactile caressing. Front. Hum. Neurosci. 8 (2014), 893. doi: 10.3389/fnhum.2014.00893.

Sowndhararajan

Kim

Influence of fragrances on human psychophysiological activity: With special reference to human electroencephalographic response. Sci. Pharm. 84(4) (2016), 724–752.

Mongia

P.K.

Sharma

R.K.

Estimation and Statistical Analysis of Human Voice Parameters to Investigate the Influence of Psychological Stress and to Determine the Vocal Tract Transfer Function of an Individual. Journal of Computer Networks and Communications. 2014, 1-17: 290147. doi: 10.1155/2014/290147.

Sigmund

Influence of psychological stress on formant structure of vowels. Elektronika ir Elektrotechnika. 18(10) (2012), 45–48.

10.

Hansen

J.H.L.

Patil

Speech Under Stress: Analysis, Modeling and Recognition. In: Müller

(ed) Speaker Classification I. Lecture Notes in Computer Science, vol 4343. Springer, Berlin, Heidelberg. 2007.

11.

Ang

, et al. Emotional prosody analysis on human voices. 2018 IEEE 8th Annual Computing and Communication Workshop and Conference (CCWC), Las Vegas, NV, 2018, pp. 737–741. doi: 10.1109/CCWC.2018.8301691.

12.

Schwartz

D.A.

Howe

C.Q.

Purves

The statistical structure of human speech sounds predicts musical universals. J. Neurosci. 23(18) (2003), 7160–8.

13.

Namazi

Akhavan Farid

Teck Seng

Complexity-based analysis of the influence of tool geometry on cutting forces in rough end milling. Fractals. 2018. doi: 10.1142/S0218348X18500780.

14.

Tapanainen

J.M.

Fractal analysis of heart rate variability and mortality after an acute myocardial infarction. Am J Cardiol. 90(4) (2002 Aug 15), 347–52.

15.

Namazi

Daneshi

Azarnoush

Jafari

Towhidkhah

Fractal-based analysis of the influence of auditory stimuli on eye movements. Fractals. 2018. doi: 10.1142/S0218348X18500408.

16.

Alipour

Namazi

Azarnoush

Jafari

Complexity-based analysis of the relation between moving visual stimuli and human eye movement. Fractals. 2018. doi: 10.1142/S0218348X19500245.

17.

Alipour

Namazi

Azarnoush

Jafari

Fractal-based analysis of the influence of color tonality on human eye movements. Fractals. 2019. doi: 10.1142/S0218348X19500403.

18.

Alipour

Menon

Namazi

Towhidkhah

Jafari

Complexity-based analysis of the relation between fractal visual stimuli and fractal eye movements. Fluctuation and Noise Letters. 2019. doi: 10.1142/S0219477519500123.

19.

Namazi

Decoding of Hand Gestures by Fractal Analysis of Electromyography (EMG) Signal. Fractals. 2018. doi: 10.1142/S0218348X19500221.

20.

Namazi

Fractal based classification of Electromyography (EMG) signal in response to basic movements of the fingers. Fractals. 2018. doi: 10.1142/S0218348X19500373.

21.

Namazi

Jafari

Decoding of simple hand movements by Fractal Analysis of Electromyography (EMG) Signal. Fractals. 2019. doi: 10.1142/S0218348X19500427.

22.

Namazi

Fractal-based classification of Electromyography (EMG) signal between fingers and hand’s basic movements, functional movements, and force patterns. Fractals. 2019. doi: 10.1142/S0218348X19500506.

23.

Kamal

S.M.

Sim

Tee

Nathan

Namazi

Complexity-Based Analysis of the relation between human muscle reaction and walking path. Fluctuation and Noise Letters. 2020. doi: 10.1142/S021947752050025X.

24.

Namazi

Jafari

Decoding of wrist movements’ direction by fractal analysis of Magnetoencephalography (MEG) signal. Fractals. 2018. doi: 10.1142/S0218348X19500014.

25.

Namazi

et al. The fractal based analysis of human face and DNA variations during aging. Biosci. Trends. 2016, 10. doi: 10.5582/bst.2016.01182.

26.

Namazi

Kiminezhadmalaie

Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA. Comput. Math. Methods Med. 2015. doi: 10.1155/2015/242695.

27.

Namazi

Kulish

V.V.

Delaviz

Diagnosis of skin cancer by correlation and complexity analyses of damaged DNA. Oncotarget. 6(40) (2015), 42623–31. doi: 10.18632/oncotarget.6003.

28.

Namazi

R.H.

Fractal-based analysis of the influence of music on human respiration. Fractals. 2017, 25. doi: 10.1142/S0218348X17500591.

29.

Mozaffarilegha

Namazi

H.R.

Ahadi

Jafari

Complexity-based analysis of the difference in speech-evoked Auditory Brainstem Responses (s-ABRs) between binaural and monaural listening conditions. Fractals. 2018. doi: 10.1142/S0218348X18500524.

30.

Mozaffarilegha

Namazi

Tahaei

A.A.

Jafari

Complexity-based analysis of the difference between normal subjects and subjects with stuttering in speech evoked auditory brainstem response. Journal of Medical and Biological Engineering. 2018. doi: 10.1007/s40846-018-0430-x.

31.

Shafiul

Babini

Sim

Tee

Nathan

Namazi

Complexity-based decoding of brain-skin relation in response to olfactory stimuli. Computer Methods and Programs in Biomedicine. 184 (2020), 105293. doi: 10.1016/j.cmpb.2019.105293.

32.

Namazi

Seifi Ala

Bakardjian

Decoding of Steady-State Visual Evoked Potentials by Fractal Analysis of the Electroencephalographic (EEG) Signal. Fractals. 2018. doi: 10.1142/S0218348X18500925.

33.

Ahmadi-Pajouh

M.A.

Seifi Alaa

Zamanian

Namazi

Jafari

Fractal-based classification of human brain response to living and non-living visual stimuli. Fractals. 26(5) (2018), 1850069.

34.

Namazi

Khosrowabadi

Hussaini

Habibi

Akhavan Farid

Kulish

V.V.

Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal. Oncotarget. 7 (2016), 56120–56128.

35.

Alipour

J.M.

Khosrowabadi

Namazi

Fractal-based analysis of the influence of variations of rhythmic patterns of music on human brain response. Fractals. 26(5) (2018), 1850080.

36.

Namazi

Jafari

Age-based variations of fractal structure of EEG signal in patients with epilepsy. Fractals. 26(4) (2018), 1850051.

37.

Namazi

Jafari

Estimating of brain development in newborns by fractal analysis of sleep Electroencephalographic (EEG) Signal. Fractals. 27(3) (2019), 1950021.

38.

Namazi

Kulish

V.V.

Hussaini

Delaviz

, et al. A signal processing based analysis and prediction of seizure onset in patients with epilepsy. Oncotarget. 7 (2016), 342–350.

39.

Namazi

Aghasian

Seifi Ala

Fractal-based classification of Electroencephalography (EEG) signals in healthy adolescents and adolescents with symptoms of schizophrenia. Technology and Health Care. 27(3) (2019), 233–241.

40.

Namazi

Seifi Ala

Aghasian

Complexity-based classification of EEG signal in normal subjects and patients with epilepsy. Technology and Health Care. 2019, 1–10. doi: 10.3233/THC-181579.

41.

Namazi

Seifi Ala

Kulish

Decoding of upper limb movement by fractal analysis of Electroencephalogram (EEG) Signal. Fractals. 26(5) (2018), 1850081.

42.

Namazi

Ala

T.S.

Decoding of simple and compound limb motor imagery movements by fractal analysis of Electroencephalogram (EEG) signal. Fractals. 27(3) (2019), 1950041.

43.

Mujib Kamal

, et al. Decoding of the relationship between human brain activity and walking paths. Technology and Health Care. 2019, 1–9. doi: 10.3233/THC-191965.

44.

Maragos

Potamianos

Fractal dimensions of speech sounds: Computation and application to automatic speech recognition. J. Acoust. Soc. Am. 105(3) (1999), 1925–32.

45.

Véhel

J.L.

Daoudi

Lutton

Fractal modeling of speech signals. Fractals. 2(3) (2014), 379–382. doi: 10.1142/S0218348X94000478.

46.

Almenar

Abiol

Fractal prediction in waveform coding of speech signals. 2000 10th European Signal Processing Conference, Tampere, 2000, pp. 1–4.

47.

Little

M.A.

, et al. Exploiting nonlinear recurrence and fractal scaling properties for voice disorder detection. Biomedical Engineering Online. 6 (2007), 23. doi: 10.1186/1475-925X-6-23.

48.

Spangler

, et al. Fractal features for automatic detection of dysarthria. 4th IEEE EMBS International Conference on Biomedical and Health Informatics, BHI 2017 – Orlando, United States. 2017, pp. 437–440.

49.

Pitsikalis

Maragos

Analysis and classification of speech signals by generalized fractal dimension features. Speech Communication. 51(12) (2009), 1206–1223. doi: 10.1016/j.specom.2009.06.005.

50.

Alipour

Namazi

Azarnoush

Jafari

Complexity-based analysis of the influence of visual stimulus color on human eye movement. Fractals. 2018. doi: 10.1142/S0218348X19500026.

51.

Namazi

Akhavan Farid

Seng

C.T.

Fractal-based analysis of the influence of cutting depth on complex structure of cutting forces in rough end milling. Fractals. 2018. doi: 10.1142/S0218348X18500688.

52.

Kiew

C.L.

Brahmananda

Islam

K.T.

Lee

H.N.

Venier

S.A.

Saraar

Namazi

Complexity based analysis of the relation between tool wear and machine vibration in turning operation. Fractals. 2019. doi: 10.1142/S0218348X20500188.

53.

Kiew

C.L.

Brahmananda

Islam

K.T.

Lee

H.N.

Venier

S.A.

Saraar

Namazi

Analysis of the relation between fractal structures of machined surface and machine vibration signal in turning operation. Fractals. 2019. doi: 10.1142/S0218348X2050019X.

54.

Qadri

M.O.

Namazi

Fractal-based analysis of the relation between surface finish and machine vibration in milling operation. Fluctuation and Noise Letters. 2019. doi: 10.1142/S0219477520500066.

55.

Thasthakeer

A.T.

Namazi

Akhavan Farid

Teck Seng

Analysis of the correlation between fractal structure of cutting force signal and surface roughness of machined workpiece in end milling operation. Fractals. 2018. doi: 10.1142/S0218348X19500130.

56.

Hendrickson

J.B.

Huang

Toczko

A.G.

Molecular complexity: A simplified formula adapted to individual atoms. J. Chem. Inf. Model. 27 (1987), 63–67.

57.

Seetharaman

Namazi

, and Kulsih

V.V.

Phase lagging model of brain response to external stimuli – modeling of single action potential. Comput. Biol. Med. 42 (2012), 857–862.

58.

Namazi

Kulish

V.V.

Mathematical modeling of human brain neuronal activity in the absence of external stimuli. Journal of Medical Imaging and Health Informatics. 2(4) (2012), 400–407.

59.

Namazi

Kulish

V.V.

Wong

Nazeri

Mathematical based calculation of drug penetration depth in solid tumors. Biomed. Res. Int. 2016 (2016), 8437247. doi: 10.1155/2016/8437247.

60.

Namazi

Kulish

V.V.

Fractional diffusion based modelling and prediction of human brain response to external stimuli. Comput. Math. Methods Med. 2015 (2015), 148534. doi: 10.1155/2015/148534.