# Research on the UAV Sound Recognition Method Based on Frequency Band Feature Extraction
## 2 Method and Model Establishment
### Frequency Band Feature Extraction Method of UAV Sound
#### 2.2.3 Frequency Band Feature Extraction Algorithm  
Frequency band feature extraction is an improved method derived from MFCC for UAV acoustic applications. When using MFCC for feature extraction, the Mel filter bank employs a nonlinear distribution of center frequencies, densely spaced at lower frequencies  
Figure 1: Flowchart of frequency band feature extraction. and sparsely at higher frequencies. Because the Mel scale is designed to simulate the nonlinear perception of sound by the human ear, it is more sensitive to the perception of human voice, and the frequency of human voice is generally 65-1100 Hz. Under a sampling frequency of 48 kHz, the Mel filter bank exhibits the highest density below 1000 Hz, a moderate density between 1000 Hz and 2000 Hz, and a sparse distribution above 2000 Hz. However, experimental analysis reveals that UAV acoustic signatures span a broader frequency range, with harmonic components extending from a fundamental frequency of approximately 200 Hz up to 6000 Hz, and even reaching 12,000 Hz for smaller propellers. The core components of the Mel filter bank include the center frequency distribution of the filter bank and the filter functions. The nonlinear function governing the center frequency distribution is the Mel scale transformation function: Equation (8). \[f_{mel}=2595\text{log}_{10}\bigg{(}1+\frac{f_{lz}}{700}\bigg{)} \tag{8}\]  
Here \(f_{lz}\) is the Hertz scale frequency, and \(f_{mel}\) is the Mel scale frequency. The center frequencies of the filter bank are computed by uniformly distributing the required number of filters on the Mel scale and subsequently converting these points back to the Hertz scale via the inverse transformation. The mathematical formula is expressed as Equation (9). \[f_{mel}(f_{c}(n))=\frac{n}{N+1}[f_{mel}(f_{L})+f_{mel}(f_{H})] \tag{9}\]  
where \(f_{L}\) and \(f_{H}\) define the frequency range, \(N\) is the number of filters, and \(f_{c}\) represents the center frequency function of the filter bank. Based on analysis of UAV frequency distributions and Mel filter bank characteristics, a critical improvement to the feature extraction algorithm lies in replacing the speech-optimized Mel filter bank with a filter bank better suited for UAV acoustic bands. First, we define a piecewise linear function as Equation (10). \[f_{ufb}(x)= \begin{cases}w_{0}(x-x_{0})+f_{0},x_{0}\leq x\leq x_{1}\\ w_{1}(x-x_{1})+f_{1},x_{1}<x\leq x_{2}\\ w_{2}(x-x_{2})+f_{2},x_{2}<x\leq x_{3}\\ w_{3}(x-x_{3})+f_{3},x_{3}<x\leq x_{4}\\ w_{4}(x-x_{4})+f_{4},x_{4}<x\leq x_{5}\end{cases}  \tag{10}\]  
where \(x_{i}\) represents the frequency points of each frequency band, and the slope of each linear part \(w_{i}\) represents the filter density weight of the frequency segment where the function is located. The restriction formula must be met to maintain the continuity and reversibility of the function. \[\left\{ \begin{array}{llll}f_{0}&=0\\ f_{i}&=f_{ufb}(x_{i}),&i&=1,2,3,4\\ w_{i}&\
eq 0,&i&=0,1,2,3,4\end{array} \right. \tag{11}\]  
According to frequency band distribution of UAV sounds, minimal slope weights are applied in frequency bands below the motor's fundamental frequency to further suppress low-frequency noise. In frequency bands above the fundamental frequency, distinct slope weights are assigned according to UAV sound spectral density. Similarly, in frequency bands exceeding the maximum harmonic frequency, reduced slopes are implemented to attenuate high-frequency noise. The specific slope weights and corresponding frequency band partitions are detailed in Table 1.  
Finally, the piecewise function undergoes normalization to ensure data consistency, where the original slopes explicitly reflect density weighting. Using the normalized frequency transformation function, uniformly spaced frequency points are generated on the transformed scale and then converted back to Hertz scale frequencies using the inverse function to determine the center frequencies of the filter bank. The calculation formula for the center frequency is Equation (12).