## 2 Methods
### Feature Extraction  
The next step entails extracting audio features from time series of audio signals. Extracting features allows us to obtain lower-dimensional compact statistical representations while preserving the distinguishing characteristics of the signal in a non-redundant manner. In addition to reducing the computational costs, feature extraction can maximize the classification performance of the system [20]. Studies have shown that aggregated features allow us to achieve a better classification performance compared to a single feature [21]. In this contribution, we employ the spectral centroid, the spectral rolloff, the zero-crossing-rate, Spectral Bandwidth, the root-mean-square energy (RMSE), and the Mel-frequency-cepstral-coefficients (MFCCs) as features. Since signal statistics change rapidly, bird sounds, like audio signals in general, are non-stationary signals. For this reason, feature extraction is performed in a short-term processing manner where the signal is chunked into short analysis frames. The analysis frames are assumed to be in a quasi-stationary state [22]. In order to preserve as much information and arrive at a sufficient trade-off between the frequency and temporal resolution, we selected an analysis frame size of 512 samples (23 ms) while allowing an overlap of 25%. Therefore, the spectral features described below are computed frame wise. In the case an additional splitting into even shorter windows within each analysis frame is required (e.g., for the MFCC), the temporal average of the feature is computed to generate a single value that is associated with the respective analysis frame. For each MFCC, the variance of the coefficients within the analysis frame is also computed and used as an additional feature. In more detail, all features are computed using the Librosa 0.6 audio processing package [17] and can be described as follows [22]:  
Figure 1: Schematic for the bags-of-birds approach. * _Spectral Centroid:_ The spectral centroid measures the frequency where the energy of a spectrum is centered. In other words, it localizes the center of mass of the spectrum and is calculated as a weighted mean of the frequencies that the signal is composed of: \[s_{c}=\frac{\sum_{k}S(k)f(k)}{\sum_{k}S(k)},\] (1) where \(S(k)\) is the spectral magnitude at frequency bin \(k\), and \(f(k)\) represents the center frequency of the bin [23]. * _Spectral Rolloff:_ The spectral rolloff gives the frequency \(f(k)\), below which, a predefined percentage (usually set to 85%) of the total spectral energy is concentrated [24]. * _Zero-Crossing Rate:_ The zero-crossing rate \(r\) measures the smoothness of a signal. It is the rate at which a signal changes its sign from negative to positive or vice versa [25]. * _The root-mean-square energy (RMSE):_ The root-mean-square energy of a signal gives the signal's total energy and is defined as: \[e_{rms}=\sqrt{2\sum_{k}|S(k)|^{2}},\] (2) where \(S(k)\) is the spectral magnitude at frequency bin \(k\)[17]. * _Spectral Bandoitl:_ measures if the power spectrum is concentrated around the spectral centroid or spread across the spectrum. It is computed as: \[s_{b}=\sqrt{\frac{\sum_{k}(k-s_{c})^{2}\cdot|S(k)|^{2}}{\sum_{k}|S(k)|^{2}}},\] (3) where \(s_{c}\) is the spectral centroid, \(S(k)\) is the spectral magnitude at frequency bin \(k\)[26]. * _Mel-Frequency Cepstral Coefficients (MFCCs):_ Mel-Frequency Cepstral Coefficients are inspired by human auditory perception. After computing the Fourier transform of a signal, the magnitude spectrum is projected to the Mel scale, which emphasizes relevant frequencies in a non-linear way--a small bandwidth at low frequencies and large bandwidth at high frequencies. The Mel scale approximates human auditory response better than linearly spaced frequency bands. The output is log transformed, and MFCCs are obtained by taking a discrete cosine transform of the logarithmic outputs [27]. In this contribution, the analysis frames are split into windows of lengths 512 and compute the first 20 MFCC values as features in our system.