The frequency corresponding to the MFCC is the Mel frequency, which is recorded as f m e l , and its functional correspondence with frequency f is as follows: f m e l = 2595 × lo g 10 ( 1 + f 700 ) (2.1)

The following is the extraction process of the Mel frequency cepstral coefficient:

1) First, the original speech signal s ( n ) is sampled at the sampling frequency of 44.1 KHz and quantized in the 16bit mode, and then, the background noise and high-frequency noise are eliminated by using a bandpass filter. Finally, the time domain signal x ( n ) is obtained by using a pre emphasis technology to compensate the high-frequency loss of sound. Then, it is transformed by formula Eq. 2.2 to obtain the corresponding linear spectrum X ( k ) , where k is the time domain frequency corresponding to each point of the original speech signal.

A group of triangular bandpass filter combinations constitute Mel filter banks, where, 0 ≪ m ≪ M , and M is the total number of triangular filters in Mel filter banks. The center frequency of these filters is   f ( m ) . Considering the logarithmic conversion relationship between the Mel frequency and ordinary frequency, it can be seen that the center spectrum of each filter with an equal interval linear distribution in the Mel frequency is dense in the low-frequency band and sparse in the high-frequency band. The schematic diagram of the Mel frequency filter bank is shown in Figure 2.

The transfer function of each bandpass filter is as follows: H m ( k ) = { 0                                                                                           ( k < f ( m − 1 ) ) k − f ( m − 1 ) f ( m ) − f ( m − 1 )                     ( f ( m − 1 ) ≤ k ≤ f ( m ) ) f ( m + 1 ) − k f ( m + 1 ) − f ( m )                     ( f ( m ) < k < f ( m + 1 ) ) 0                                                                                               ( k > f ( m + 1 ) ) (2.3)

The formula for obtaining the logarithmic spectrum S ( m ) is as follows: S ( m ) = ln ( ∑ k = 0 N − 1 | X ( k ) | 2 H m ( k ) ) ,   0 ≤ m < M (2.4)

3) By substituting the above logarithmic energy into the discrete cosine transform (DCT), the Mel cepstral parameters C ( n ) of order L can be obtained, as shown in Eq. 2.5, where L is the order of MFCC coefficients, usually is 12–16, and M is the number of Mel filters.

Figure 3 is a 12-order MFCC characteristic diagram of a giant panda voice, in which the X-axis represents the order of the MFCC coefficient, the Y-axis represents the number of frames of voice, and the Z-axis represents the corresponding cepstral parameter value.

The standard MFCC parameters reflect the static characteristics within each frame of speech, while the difference of the MFCC reflects the dynamic characteristics. The Furui experiment shows that adding dynamic characteristics to the features can greatly improve the system performance [13]. The introduction of differential features has a wide range of applications and good results in the field of human voice recognition. Therefore, this method is also first used in the processing of giant panda voice.

After obtaining the MFCC parameters, use Eq. 2.5 to extract the MFCC first-order differential parameter Δ MFCC . D t = { C t + 1 − C t         t < θ ∑ θ = 1 Θ θ ( C t + θ − C t − θ ) / ( 2 ∑ θ = 1 Θ θ 2 )   e l s e C t − C t + 1     t ≥ T − Θ   (2.6) where D t represents t-th ΔMFCC, T is the order of the cepstral coefficient, Θ is the time difference of the first derivative, and the values of 1 and 2 represent the first cepstral coefficient [14].

Figure 4 shows the characteristics of the MFCC of order 12 and ΔMFCC of order 12 of the same giant panda voice.

The IMFCC feature can compensate the high-frequency information and improve the system recognition rate through its integration with the traditional MFCC. The structure of the IMFCC filter bank is shown in Figure 5.

Corresponding to the Mel domain of the traditional filter structure, we call this domain as the inverted Mel domain, which is recorded as IMEL, and the corresponding frequency is recorded as F i m e l . The relationship with the time domain is as follows: F i m e l ( f ) = 219.268 − 2595 l o g 10 ( 1 + 4031.25 − f 700 ) (3.1)

The inverted filter response becomes E H i ( k ) = H p + i + 1 ( N 2 − k + 1 ) (3.2) where E H i ( k ) is the filter response in the MEL domain.

Figure 6 shows the 12th order MFCC and the 12th order IMFCC characteristic diagram of a giant panda sound, in which the X axis represents the order of the MFCC , the Y axis represents the number of voice frames, and the Z axis represents the corresponding cepstral parameter values.

MFCC characteristic parameters are obtained through the Mel filter bank and a series of operations. Accordingly, the characteristic coefficients obtained after a series of operations through the Mel filter bank and composite filter bank of the inverted Mel filter bank are called composite Mel frequency cepstral coefficients, which are recorded as the CMFCC (compound Mel frequency cepstral coefficient).

Therefore, we fuse the 12th order MFCC characteristic diagram and 12th order IMFCC characteristic diagram in Figure.7 to obtain the corresponding 24th order CMFCC characteristic parameter diagram, as shown in Figure 8.

Assuming that the sequence composed of CMFCC features satisfies the fractional Brownian motion distribution, we can calculate H according to the following method [13, 15, 16].

Let n be the number of data of CMFCC-modified multifractional Gaussian noise (mmfGn) [8, 9]. Let 1 < k < N be the length of the neighborhood used for estimating the function parameter. We will estimate H ( t ) only for t   i n   [ k N , 1 − k N ] .

Without loss of generality, we assume m = N / k to be an integer. Then, our estimator of H ( i ) is the following: H ^ i = − log [ π 2 S k , N ( i ) ] log ( N − 1 ) , (3.3) where S k , N ( i ) = m N − 1 ∑ j ∈ [ i − k 2 , i + k 2 ] | X j + 1 , N − X j , N |   (3.4)

Figure 8 shows the original sound signal of giant panda and the CMFCC characteristic sequence. Figure 9 shows the H-index distribution of two CMFCC characteristic sequences of the giant panda sound. In Figure 9A, the giant panda sound duration time T = 2 s , sampling frequency f s = 192 k H z , n = 7608 , and k = 512 . In Figure 9B, the giant panda sound duration T = 9 s , sampling frequency f s = 44.1 k H z , n = 7940 , and k = 512 . The experimental results show that the CMFCC characteristic sequence of the giant panda voice has long-range dependent characteristics.