# Acoustic Classification of Singing Insects Based on MFCC/LFCC Fusion
## 3 Segmentation and Feature Extraction
### Feature Extraction  
In order to develop an efficient pattern recognition system, a sound parameterization technique designed specifically for acoustic identification and classification of acoustic sounds of insects is applied in this work. This technique is based on MFCC and LFCC. These parameters are forwarded as feature vectors to the machine learning algorithm to carry out taxonomic identification.  
The LFCC is a linear cepstral representation of sound. This representation is known as cepstrum and is the result of taking the Discrete Fourier Transform (DFT) of the logarithm of the estimated spectrum of a signal. These linear coefficients have been calculated using a linear filter bank, which has better resolution in higher frequency regions. The MFCC is based on a nonlinear cepstral representation of the signal equally spaced on the Mel scale. This scale approximates the response of the human auditory system more closely than linear-spaced frequencies [22]. The transformation from Hertz to Mel scale is determined by the following equation:  
\[mel=2595\log_{10}\left(\frac{f}{700}+1\right) \tag{2}\]  
For both, LFCC and MFCC computation, a window size of 20 ms has been selected with an overlap of the window segments of 33%. The MFCC used in this proposal are calculated based on  
Figure 1: Example of two insect sound spectrograms.  
the method of [PERSON] et al. [23], with some parameter adjustments to obtain better results from these coefficients. In this study, Mel filter bank consists of 40 triangular filters. The length of MFCC for each frame is \(L=18\). Finally, the average MFCC over all frames is calculated as:  
\[f_{m}=\sum_{n=1}^{N}\left(C_{m},n\right)/N,0\leq m\leq L-1 \tag{3}\]  
where \(f_{m}\) is the \(m\)th Mel coefficient, and \(N\) is the number of frames.  
To calculate the LFCC, a log energy filter bank has been applied to the discrete cosine transform as shown in (4), where j denotes the index of the linear frequency cepstral coefficients, \(X_{i}\) is the log-energy output from the \(i\)th filter, B is the number of triangular filters and M the number of coefficients to compute.  
\[LFCC_{j}=\sum_{i=1}^{B}X_{i}\cos\left(j\left(i-1/2\right)\pi/B\right),j=0\dots M \tag{4}\]  
The proposed approach in this work is based on a data fusion of the MFCC and LFCC in order to obtain a more robust sound parameterization of insect sounds. The data fusion technique consists of creating a matrix of data with both LFCC and MFCC. This matrix is formed by horizontally concatenating the MFCC data matrix and the LFCC data matrix as shown in (5). Each row of the matrix represents a segmented syllable and the columns are the MFCC and LFCC extracted by each syllable, merged horizontally. Most insects can produce sounds in frequencies anywhere in the spectrum, forcing the system to find the right useful information at many ranges of the acoustic spectrum. These two types of cepstral coefficients have been selected to be fused because several species of insects produce their sounds at higher frequencies and other at lower frequencies. Thus, a representation the acoustic signal information with a high degree of precision is reached.  
\[Parameters\ =\ \left[\ MFCC\ LFCC\ \right] \tag{5}\]