# An Analysis of Sound Event Detection under Acoustic Degradation Using Multi-Resolution Systems
## 2 Materials and Methods
### Multiresolution Analysis  
Each sound event category shows different temporal and spectral characteristics. This fact is easily illustrated by the different durations of the event categories, shown in Table 2. Therefore, to improve SED performance, our main idea is that different time-frequency resolutions would be more suited to detect different types of events. Thus, combining the information of several mel-spectrogram features extracted at different resolution points should lead to a better overall performance [37].  
Aiming to test this hypothesis, we defined five different time-frequency resolutions, taking as a starting point the resolution used by the baseline system, which we called _BS_. Each resolution point is defined by a set of values for the parameters of feature extraction: Fast Fourier Transform (FFT) length (\(N\)), window length (\(L\)), window hop (\(R\)) and number of filters in the Mel filterbank (\(n_{mel}\)). Due to the feature extraction process, there is a compromise between temporal resolution and frequency resolution. For instance, increasing the length of the window (\(L\)) allows a finer frequency analysis, but implies obtaining a lower time resolution. Hence, we propose a resolution point with twice better time resolution than the baseline, which we call \(T_{++}\), and a resolution point with twice better frequency resolution than the baseline, which we call \(F_{++}\). In the intermediate points between each of these points and \(BS\), we define \(T_{+}\) and \(F_{+}\), respectively. The parameters of the five resolution points are described in Table 3.  
To obtain multiresolution systems, firstly, we trained single-resolution systems, which were based on the DCASE Challenge baseline and modified to operate on each of the different resolution points by adapting the sizes of the pooling layers in the convolutional stage. Then, we performed a model fusion averaging the score sequences given by systems trained with different resolutions before the application of the threshold and the median filter. Using this method, we obtained a three-resolution system which combines the _BS_ resolution with \(T_{++}\) and \(F_{++}\), denoted as _3 res_ in this paper, and a five-resolution system combining all the mentioned resolutions, denoted as _5 res_.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Event Class** & **Mean (s)** & **Std. (s)** \\ \hline Alarm/bell/ringing & 2.42 & 2.88 \\ Blender & 5.57 & 2.87 \\ Cat & 1.05 & 1.05 \\ Dishes & 0.57 & 0.69 \\ Dog & 0.72 & 0.92 \\ Electric shaver/toothbr. & 5.43 & 3.24 \\ Frying & 8.72 & 2.09 \\ Running water & 6.37 & 3.60 \\ Speech & 1.36 & 1.10 \\ Vacuum cleaner & 8.31 & 2.20 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean and standard deviations of durations of sound events in DESED Public Evaluation set, computed for each target category.  
Figure 1: Block diagram showing structure of Sound Event Detection baseline system. First step is extraction of mel-spectrogram features from audio waveform. Mel-spectrograms are fed into Convolutional Recurrent Neural Network, which is composed of a convolutional stage (CNN), a recurrent stage (RNN), and an attention pooling module. Outputs of CRNN are \(K\) score sequences, one for each target category (\(K=10\)). Finally, to compute \(F_{1}\) score, score sequences are converted into binary values using a threshold of 0.5, and then smoothed with a median filter of 0.45 s.  
Through the use of the _3 res_ and _5 res_ systems, we were able to outperform the single-resolution baseline system in the DCASE 2020 Challenge task 4 [37; 38]. The improvement of performance in terms of macro \(F_{1}\) score was observed over the DESED Validation set and the DESED Public evaluation set. The _5 res_ system was submitted to the evaluation and outperformed the baseline system over the DESED 2020 Evaluation set.