Gamma Binaural Beats and its Quality Assessment

 

Ali Jassim Mohamed Ali, Fatin E. M. Al-Obaidi

Department of Physics, College of Science, Mustansiriyah University, Baghdad, Iraq.

 

ABSTRACT:

Due to brain's internal wiring, a beating effect will be created in it as soon as two sine waves with slightly different frequencies be applied to each ear. Brain's response to such beat remains controversial; therefore and in addition to author's desire toward investigate the role of beat and carrier frequencies upon the brain, this research introduces a new way for quantifying such phenomenon by using an objective methods of quality assessment. In such method, the criteria of error visibility (differences) between tones had been tested. Gamma wave had been used here to investigate its beat and carrier frequencies effects inside the brain. The reversal relationship between (carrier-beat) frequencies activates uponStructural Similarity Index Metric (SSIM) andStructural Dissimilarity Metric (DSSIM) values. After all and in order to detect the best series in Gamma brain waves to investigate and quantize, carrier frequency produces a meaningful variation than beat frequency one.

 

 

 

1. INTRODUCTION:

The dichotic presentation of two nearly equivalent pure tones with slightly different frequencies lead to what we called 'beat' in the brain. The beat in this case generated within the brain and is referred to as a 'binaural beat' [1,2]. When a tone of 410Hz presented to the right ear as an example and a 420Hz one to the left, then a beat of 10Hz shall be perceived and located in the brain with carrier frequency of 415Hz [2,3]. In general, binaural beat can occurred if the carrier frequency of the left and right stimulus is no longer than 1500Hz with a difference of the two tones which not exceed 50Hz [4,5]. In 1839, H. W. Dove discovered the concept of binaural beat and then outlined with more details by G. Oster over five decades ago [6-8]. The authors in [8] found that binaural beat audio has the role in decreasing acute pre-operative anxiety affectively.

 

 

For inducing a meditative state, [1] suggested that 6-Hz binaural beat on a 250Hz carrier tone can be regard as a good stimulus. T. Mihajloski et al in [4] developed a new procedure of evoking transient Auditory Evoked Potentials to binaural beats by adopting frequency modulated stimuli. Table (1) summarizes brain wave with its four bands.

 

Table(1) Brain waves types [3]

 

Quality review is one of the challenging fields in many application areas [9]. The quality engineering method for an example of Taguchi employing of experiment provides an efficient and systematic way to determine an optimal welding parameter in the submerge arc welding [10]. Otherwise, the authors in [11] used six different methods to estimate Air Quality Index (AQI) to compare the prevailing ambient air quality in the study area. AR Warade et. al. in [12] found that the fugitive emission have a significant role on the ambient air quality. N. G. Telkapalliwar in [13] made an analysis of groundwater quality parameters in ten different villages from Arvi region of Wardha district of Maharashtra. S. K. Dixit et. al. investigated in [14] the groundwater quality in rural areas of Karwi, Chitrakoot. The study reported some other parameters which exceeded the permissible limit and hence can be considered to be unsuitable for drinking purposes. A physic-chemical analyse for ground and drinking water quality has been studied by A. K. Tiwari as in [15]. In this study, the author found some other important parameters that exceeded the permissible range and it is also unsuitable for drinking purposes. Several cases of dental and skeletal fluorosis have appeared with alarming rate in [16] found in some villages in India due to the higher fluoride level in the drinking water. In the field of image processing, the method used by O. Barapatre et. al. in [17] improves image quality in terms of feature improvement and image stylization. The statistical used methods by N. K. Dewangan et. al. in [18] can be used to determine an overall quality measure of the compression method. So, the goal of quality assessment algorithms is to automatically assess the quality of an image, wave or videos in addition to an  agreement with human quality judgments [9].

 

In this research, an attempt to visualize Gamma brain waves has been chosen to test by utilizing quality assessment. The latter is a crucial need which is closely related to signal differences assessment in which quality is based on the differences between left and right tones [19,20].

 

Due to certain considerations related to its cost, an objective method is seems to be more preferable than the subjective one in the quality process [21].

 

2. OBJECTIVE QUALITY ASSESSMENT:

2.1 Human Visual System (HVS):

Feature Based Metrics:

2.1.1 Structural Similarity Index Metric (SSIM):

This measure compares two signals using information about luminous, contrast and structure as follow [19,20]:

 

                      (1)

 

                     (2)

 

                          (3)

 

Where x and y are two different positions in two separate signals, mx, sxand sxyare the average of x, standard deviation of x, and the covariance of x and y respectively where [22]:

 

                (4)

 

       (5)

 

 

  (6)

 

Where w(p,q) is a Gaussian weighting function such that:

 

                                      (7)

 

And C1, C2 and C3 are constants given by [22,23]:

C1=(K1L)2                                                                  (8)

C2=(K2L)2                                                                  (9)

and

C3=C2/2                                                                     (10)

 

L is the dynamic range for the sample data and K1áá1 and K2áá1 are two scalar constants. Throughout this research a value of 0.01 and 0.03 are set to parameter K1 and K2 respectively [22]. The structure similarity can be written as [23]:  

 

           (11)

 

SSIM is a decimal value between (-1,1) [24]. 

 

2.1.2 DSSIM:

This is the structural dissimilarity metric which is derived from SSIM as follows [24]:

 

                          (12)

 

The greater values of SSIM and DSSIM refer to greater similarity between signals [20].

 

3. RESULTS:

In this research, Gamma sine tones had been adopted through the web site found in [3]. A general preview for the used waves can be summarized in Table(2).

 

 

Table(2) Gamma brain wave generated by [3]

 

Figure (1) shows SSIM and DSSIM relationships with carrier and beat frequencies for Gamma waves respectively.

 

Due to the inverse relationship between beat and carrier frequencies as explained in Table(2), results show a reversal behavior for both SSIM and DSSIM toward increasing carrier and beat frequencies respectively. The SSIM variation with increasing carrier frequency as in Fig.(1a) takes a shape of a crest reaches its highest value in the middle series (i.e. 1027.75-1032Hz). This variation and according to the inverse relation between beat and carrier frequencies reversed in Fig, (1c). Figure(1b) indicates DSSIM variation with increasing carrier frequency. The variation seems to take a Gaussian shape which lies in the series (1022.75-1032) Hz with beats (41-54.5) Hz as in Fig.(1d) reaching its highest value at carrier frequency equal to 1029Hz with beat frequency 52Hz.After all, It appears that carrier frequency variation is more suitable to quantize Gamma waves than using beat's frequency variation.

 

 

(a)

 

 

(b)

 

(c)

 

(d)

Fig.(1) Gamma brain wave relationships with carrier and beat frequencies

Blue series for range (1022.75-1024.5) Hz

Red series for range (1025.25-1027.5) Hz

Green series for range (1027.75-1032) Hz

Magenta series for range (1030.25-1034.5) Hz

 

4. CONCLUSION:

According to the reversal relation between them, results show a special behavior for carrier and beat frequencies for Gamma brain wave. This affected SSIM and DSSIM variations with beat and carrier frequencies. Among the various Gamma brain wave series, one can utilized carrier frequency variation in detecting the useful and meaningful range (series) than beat variation.

 

5. FUNDING STATEMENT:

The research did not receive any specific funding but was performed as part of the employment of the authors.

 

6. REFERENCES:

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Accepted on 20.09.2018        © RJPT All right reserved

Research J. Pharm. and Tech 2018; 11(11): 4842-4845.