In this research, a biometric speech coding method is developed where empirical wavelet transform is used to extract biometric features of speech signals for voice identification of the speaker. This method differs from existing methods because it uses a set of adaptive bandpass Meyer wavelet filters and Hilbert spectral analysis to determine the instantaneous amplitudes and frequencies of internal empirical modes. This makes it possible to use multiscale wavelet analysis for biometric coding of speech signals based on an adaptive empirical wavelet transform, which increases the efficiency of spectral analysis by separating high-frequency speech oscillations into their low-frequency components, namely internal empirical modes. Also, a biometric method for encoding speech signals based on mel-frequency cepstral coefficients has been improved, which uses the basic principles of adaptive spectral analysis using an empirical wavelet transform, which also significantly improves the separation of the Fourier spectrum into adaptive bands of the corresponding formant frequencies of the speech signal.
The development of new methods and means of ensuring information security is intended
primarily to prevent threats of access to information resources by unauthorized persons. To solve
this problem, it is necessary to have identifiers and create identification procedures for all users.
Modern identification and authentication include various systems and methods of biometric
identification [
One of the most common biometric characteristics of a person is his or her voice, which has a
set of individual characteristics that are relatively easy to measure (e.g., the frequency spectrum of
the voice signal). The advantages of voice identification also include ease of application and use,
and the fairly low cost of devices used for identification (e.g., microphones) [
Voice identification capabilities cover a very wide range of tasks, which distinguishes them
from other biometric systems. First of all, voice identification has been widely used for a long time
in various systems for differentiating access to physical objects and information resources. Its new
application in systems based on telecommunication channels seems promising. For example, in
mobile communications, voice can be used to manage services, and the introduction of voice
identification helps protect against fraud [
Voice identification also plays an important role in solving such an important task as protecting
speech information. This identification is used to create new technical means and software and
hardware devices for protecting speech information, in particular, from leakage through acoustic,
vibroacoustic, and other channels [
Thus, the development of new methods of voice identification is a promising and relevant scientific and technical task in providing biometric authentication in information and telecommunication systems.
The paper investigates a well-known method of biometric coding of speech signals based on
melfrequency cepstral coefficients (MFCC) [
N f−1 m=0 1 2 ), πn(m+ )
N f
n=0 , … , N f −1 ,
prologarithmized energy of the spectrum [
N−1 2 E [ m ]=ln( ∑ |X [ k ]| H m [ k ]), m=0 , … , N f −1 ,
k=0 discrete Fourier transform (DFT)
X [ k ]= ∑ x [ n ] w [ n ] e−N2πj kn , k =0 , … , N −1 ,
N−1
n=0
processed with a triangular filter [
0 ,∧k < f [ m−1] { ( f [ m+1]−k )
( k −f [ m−1]) H m [ k ]= ( f [ m ]−f [ m−1]) ( f [ m+1]−f [ m ]) 0 ,∧k > f [ m+1] ,∧f [ m−1] ≤ k < f [ m ] ,∧f [ m ] ≤ k ≤ f [ m+1] where f [ m ]=( N f ) M−1( M ( Fmin)+m M ( Fmax− Fmin) )
F s N f +1
in mel scale M =1127.01048 × ln (1+ F / 700) [
The problem is that the presented method of biometric encoding of speech signals based on
MFCC does not meet the condition of adaptability [
¿ n=1 ¿ N Λn=[ 0 , π ] ,
where Λn=[ ωn−1 , ωn ] are the segments of the Fourier spectrum [ 0 , π ] of the speech signal under
study, which is divided into N adjacent segments with boundaries ωn (where ω0=0 and ωN =π ),
which leads to suboptimal extraction of biometric features of speech signals and to a decrease in
the probability of recognizing the voice features of a person [
The developed method includes the following steps (see Fig. 1). The speech signal, whose frequency range is from 300 to 3400 Hz, is divided into K frames of 20 ms in length by N counts, which intersect at 1/ 2 frame length to ensure the stationarity of the process (see Fig. 2) [16]. w [ n ]=0.53836−0.46164 × cos(2 π
n N −1 n=0 , … , N −1.
The values of k indexes correspond to frequencies:
F f [ k ]= s k , k =0 , … , N / 2 ,
N
where F s is the sampling rate of the speech signal.
The normalized Fourier spectrum in terms of frequency [ 0 , π ] and amplitude [
Then ∀ n>0, the adaptive basis {ϕ1 (ω) , {ψn (ω)}nN=1} is set by the scaling function ϕ^n ( ω) and wavelet functions ψ^ n (ω), which corresponds to the low-pass filter and N −1 bandpass Meyer filters for each spectrum segment Λn [21].
1 ,∧|ω|≤ (1−γ ) ωn ϕ^n (ω)={cos[ π2 β( 2 γ1ωn (|ω|−(1−γ ) ωn))],∧(1−≤ γ(1) ω+γn ≤)ω|ωn |≤
0 ,∧ot h erwise 1 ,∧(1+ γ ) ωn ≤|ω|≤
≤ (1−γ ) ωn+1 (|ω|−(1−γ ) ωn+1))],∧(1−γ ) ωn+1 ≤|ω|≤
≤ (1+ γ ) ωn+1 sin [ π2 β( 2 γ1ωn (|ω|−(1−γ ) ωn))],∧(1−≤ γ(1) ω+γn ≤)ω|ωn |≤
0 ,∧ot h erwise where the function β ( x ) must meet the condition β ( x )={01 ,,∧∧ xx ≤≥ 10 and β ( x )+ β (1− x )=1
∀ x∈ [
In practice, the following polynomial function is used [22] β ( x )= x4 (35−84 x +70 x2−20 x3) . As can be seen from the scaling function ϕ^n ( ω) and wavelet functions ψ^ n ( ω), adaptability is achieved by building bandpass filters centered around the frequencies ωn, which characterize the biometrics of the speech.
Then the detailed coefficients of W εf ( n , t ) are given by scalar products with empirical wavelet functions:
W εf ( n , t )=⟨ f , ψn ⟩= ∫ f ( τ ) ψn ( τ −t ) dτ =( f^ ( ω) ψ^ n ( ω))∨ , and the approximation coefficients W εf ( 0 , t ) by a scalar product with a scaling function: ∨
W εf (0 , t )=⟨ f , ϕ1 ⟩= ∫ f ( τ ) ϕ1 ( τ −t ) dτ =( f^ ( ω) ϕ^1 ( ω)) , where ψ^ n ( ω) and ϕ^1 ( ω) are defined by the equations of the wavelet functions ψ^ n ( ω) and the scaling function ϕ^n ( ω), respectively [23–25].
The reconstruction of the speech signal f (t ) using the wavelet coefficients of detail W εf ( n , t ) and approximation W εf (0 , t ) is given by the following expression
N N ∨ f (t )=W εf (0 , t ) ϕ1 (t )+∑ W εf ( n , t ) ψn (t ) = (W^ εf (0 , ω) ϕ^1 ( ω)+∑ W^ εf ( n , ω) ψ^ n ( ω)) .
n=1 n=1 Then the internal empirical modes of the studied signal f (t ) are given by the formulas f 0 (t )=W εf ( 0 , t ) ϕ1 (t ) , f n (t )=W εf ( n , t ) ψ n (t ) , and the orthogonality of the expansion is proved by the fact that [26–28]
N f (t )=∑ f n (t ) .
n=0
To determine the instantaneous frequency and amplitude of the internal empirical modes (IEMs) of the speech signal, we will resort to Hilbert spectral analysis.
The Hilbert transform (HT) of EWT x (t ) is given by the following expression y (t )= 1 P ∫∞ x ( τ ) dτ ,
π −∞ t −τ where P is the principal Cauchy value of the singular integral [29, 30].
With the help of HT EWT x (t ) we can get an analytical signal
z (t )= x (t )+iy (t )=a (t ) eiθ(t ) , where i=(−1)1/2.
Then the instantaneous amplitude and frequency of the EWT can be expressed as a (t )=√( x2+ y2) , ω (t )=dθ / dt , where the instantaneous frequency of ω (t ) is determined by the rate of change of the instantaneous phase
θ (t )=arctan ( y / x ) , and the EWT x (t ) can be expressed as the real part of the following equation [31] n x (t )=ℜ {∑ a j (t ) exp [i ∫ ω j (t ) dt ]}.
j=1 Then the Hilbert energy density spectrum is defined as
Si , j= H (ti , ω j)= ∆ t ×1∆ ω H [∑k=n1 a2k (t )], where the intervals ∆ t × ∆ ω represent the values of a2 (t ) at a given time and frequency [32]. Let’s set the threshold function (see Fig. 4), which is described by the following expression: Let’s assume that the probability of recognizing P frequency and amplitude of the function of the harmonic distribution law x (t )= A × sin ( ωt + φ ) is 1, and the function of the uniform distribution law x (t )={b−a 1 ,∧ x∈ [ a , b ] 0 ,∧ x∉ [ a , b ] is 1/2 [34, 35].
Then the theoretical criterion for finding the maximum possible probability of recognizing the biometric speech features of the analyzed frame is written in the following way, which is based on the balance between the energy of the biometric speech features and their number √∑|Ci … N|
N 2 P= k=1 = N −i , i=1 , … N , √ ∑N|C|2 N
k=1 where C is the Hilbert energy spectrum of length N , and T =Ci [36–38].
In this system to evaluate the results of automatic recognition of voice control commands, a classifier built by the criterion of minimum distance is used. The dispersion of the difference between the mathematical expectation of the mathematical expectation of the recognition features based on the developed method of the reference voice images stored in the database and the mathematical expectation of the recognition features based on the developed method at the testing level of the system is used as such an indicator.
The variance in the difference of the difference of the mathematical expectations of two samples of voice control commands (recognition features based on the developed method), is written as follows: n where, xi is recognition features based on the developed method stored in the base of reference voice images, ¯xi Is recognition features based on the developed method at the system testing level, n is some recognition features based on the developed method.
The decision on biometric identification of voice commands is made according to the criterion of minimum variance, i.e., the smallest deviation of the compared recognition features based on the developed method in a certain recognition threshold which is given by the following expression: n n ( ∑i=1 xi ∑ D= i=1 n
n − ∑i=1 ¯xi ) n 2 , if Dmin<Θ identified ! else not identified ! end where, Dmin is the minimum variance, Θ = 1 – Δ is a given threshold of acceptable recognition (in practice, Δ = 0.80..0.90 is usually used). The minimum variance, which is within the specified threshold of acceptable recognition, is the best result of comparison, which means that the command is identified (recognized) is “identified!” Otherwise, the voice command fails biometric identification (is not recognized) and is “not identified!”
The paper details the obtained results of preliminary experimental research, based on which conclusions are drawn about the feasibility of further scientific and practical application of the system for recognizing voice control commands based on cepstral analysis and the developed algorithm for calculating the recognition features based on the developed method, as well as, a thorough justification of the scientific and technical significance of the conducted experimental research.
All scientific-experimental studies of the system of recognition of voice control commands set out below (Tables 1–3), were carried out taking into account the criterion of minimum distance, which is the variance of the difference between the mathematical expectations of the compared recognition features based on the developed method, depending on which varied values of the minimum variance Dmin, thereby giving an objective assessment of the quality (reliability) of recognition of voice control commands in the testing mode of the system. The decision on biometric identification of voice commands is made by the criterion of minimum variance Dmin in a given threshold of acceptable recognition Θ = 1 – Δ = 0.15, where Δ = 0.85. In the first experiment (Table 1), we compared the recognition features based on the developed method of voice commands of control subject No. 1: “up”, “down”, “right”, and “left”, which were stored at the training level in the base of reference voice images with the recognition features based on the developed method of voice commands of the same control subject No. 1, but already in the system testing mode (the recognition features based on the developed method of spoken voice commands in the testing mode are compared with the recognition features based on the developed method of voice commands spoken earlier in the system training mode).
From the obtained results (Table 1) it can be seen that the recognition features based on the developed method of the voice commands of the control subject No. 1 meet the criterion of minimum dispersion Dmin in the given threshold of acceptable recognition Θ = 0.15: “up” is Dmin = 0.0311, “down” is Dmin = 0.0648, “right” is Dmin = 0.0123, “left” is Dmin = 0.0112, based on this, the decision about positive biometric identification of the spoken voice commands is made (voice commands are recognized). In other cases (Table 1) it is seen that the values of Dmin do not correspond to the selected criterion, which means that the recognition features based on the developed method of the spoken voice commands do not coincide with the recognition features based on the developed method that are stored in the database of reference voice images, i.e. the voice commands are not recognized.
left In the second experiment (Table 2), we compared the recognition features based on the developed method of the spoken voice commands of control subject No. 2 in the testing mode with the recognition features based on the developed method of the voice commands of control subject No. 1 spoken earlier in the system training mode.
From the obtained results (Table 2), we can conclude that the recognition features based on the developed method of voice commands of the control subject No. 2 meet the criterion of minimum variance Dmin in a given threshold of acceptable recognition Θ = 0.15: “up” is Dmin = 0.0451, “down” is Dmin = 0.0482, “right” is Dmin = 0.0967, “left” is Dmin = 0.0703, and therefore, a decision is made about the positive result of recognizing the spoken voice commands.
In all other cases, voice commands are not recognized because the resulting values do not meet the specified recognition criterion.
In the third experiment (Table 3), the recognition features based on the developed method of the spoken voice commands of control subject No. 3 in the testing mode were compared with the Recognition features based on the developed method of voice commands of control subject No. 1 spoken earlier in the training mode of the system, which are stored in the database of reference voice images of control commands.
The obtained values of the comparison results: “up” is Dmin = 0.0602, “down” is Dmin = 0.0912, “right” is Dmin = 0.0846, “left” is Dmin = 0.0785, fully meet the criterion Dmin < Θ, where Θ = 0.15, and therefore, the decision about the positive result of recognizing the spoken voice commands is made. As for the other obtained resultant values, they do not meet the specified recognition criterion, and thus, the voice commands are not recognized.
The paper develops a method of biometric coding of speech signals based on empirical wavelet transform, which differs from existing methods by constructing a set of adaptive bandpass Meyer wavelet filters with the subsequent application of Hilbert spectral analysis to find instantaneous amplitudes and frequencies of functions of internal empirical modes, which will allow to determine biometric features of speech signals and increase the efficiency of their coding.
The paper details the results of preliminary experimental studies, based on which conclusions are drawn about the feasibility of further scientific and practical application of the developed system for recognizing voice control commands based on the novelty of cepstral analysis and the algorithm for calculating the recognition features based on the developed method, as well as, justification of the scientific significance of the study.
A comparative evaluation of the calculated values obtained according to the chosen criterion of minimum distance, which is the main indicator of the quality criterion of voice command recognition, has been carried out.
In the first experiment (Table 1) we compared the Recognition features based on the developed method of voice commands of control subject No. 1: “up”, “down”, “right”, and “left”, which were stored at the training level in the base of reference voice images with the Recognition features based on the developed method of voice commands of the same control subject No. 1, but already in the system testing mode.
From the obtained results (Table 1) we can see that the recognition features based on the developed method of voice commands of the control subject No. 1 meet the criterion of minimum variance Dmin in the given threshold of acceptable recognition Θ = 0.15: “up” is Dmin = 0.0311, “down” is Dmin = 0.0648, “right” is Dmin = 0.0123, “left” is Dmin = 0.0112, based on this, the decision about positive biometric identification of the spoken voice commands is made.
In the second experiment (Table 2), we compared the recognition features based on the developed method of the spoken voice commands of control subject No. 2 in the testing mode with the recognition features based on the developed method of the voice commands of control subject No. 1 spoken earlier in the system training mode.
From the obtained results (Table 2), we can conclude that the recognition features based on the developed method of voice commands of the control subject No. 2 meet the criterion of minimum variance Dmin in a given threshold of acceptable recognition Θ = 0.15: “up” is Dmin = 0.0451, “down” is Dmin = 0.0482, “right” is Dmin = 0.0967, “left” is Dmin = 0.0703, and therefore, a decision is made about the positive result of recognizing the spoken voice commands.
In the third experiment (Table 3), the recognition features based on the developed method of the spoken voice commands of the control subject No. 3 in the testing mode were compared with the recognition features based on the developed method of the voice commands of the control subject No. 1 spoken earlier in the system training mode. The obtained values of the comparison results: “up” is Dmin = 0.0602, “down” is Dmin = 0.0912, “right” is Dmin = 0.0846, “left” is Dmin = 0.0785, fully meet the criterion Dmin < Θ, where Θ = 0.15, and therefore, the decision about the positive result of recognizing the spoken voice commands is made.
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