## 4 Discussion  
A noise-robust speech emotion recognition model is proposed in this work. The proposed model generates an emotion probability vector for four emotions (angry, happy, sad, and neutral) from a noisy speech waveform corresponding to an utterance. The input noisy speech waveform is converted to four band-pass filtered waveforms (0\(\sim\)1 kHz, 1 kHz\(\sim\)2 kHz, 2 kHz\(\sim\)4 kHz, and 4 kHz\(\sim\)8 kHz) by using 401-tap FIR filters. The model consists of a multi-decoder Wave-U-Net and an emotion classifier. The multi-decoder Wave-U-Net of this work is composed of the band-pass filters, 4\(\times\) up-samplers, a five-stage down-sampling encoder, a 2-layer LSTM, six five-stage up-sampling decoders, skip-nets, and 4\(\times\) down-samplers. The noisy speech waveform input has the shape of [T] at the sample rate of 16,000 Samples/s, the following band-pass filters generate a [T,4] shaped signal, the following 4\(\times\) up-samplers generate a [4T, 4] shaped signal, the following encoder generates a [T/256, 320] signal, then the 2-layer LSTM generates a [T/256, 320] signal, then the six decoders generate a [4T, 6] signal, and then the 4\(\times\) down-samplers generate a [T, 6] signal. The outputs of the six decoder blocks ([T, 6]) consist of four band-pass filtered waveforms, one pitch-related waveform, and one emotion classifier \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Removing Component**} \\ \cline{2-7}  & **-** & **0\(\sim\)1 kHz** & **1 kHz\(\sim\)2 kHz** & **2 kHz\(\sim\)4 kHz** & **4 kHz\(\sim\)8 kHz** & **Pitch** \\ \hline Avg. acc. (\%) & 63.0 & 58.1 & 59.0 & 60.8 & 60.5 & 61.1 \\ Acc. deg. (\%) & 0 & \(-\)4.9 & \(-\)4.0 & \(-\)2.2 & \(-\)2.5 & \(-\)1.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average accuracy for different SNRs of the ablation study models in Table 6 and the accuracy degradation from the proposed model. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Training Dataset**} & \multicolumn{6}{c}{**Accuracy (\%)**} \\ \cline{2-7}  & **Clean** & **20 dB** & **5 dB** & **0 dB** & \(-\)**3 dB** & \(-\)**6 dB** \\ \hline IEMOCAP & 47.2 & 47.3 & 46.3 & 45.3 & 45.1 & 44.6 \\ ESD * [31] & 48.7 & 48.8 & 48.4 & 47.5 & 46.1 & 44.3 \\ IEMOCAP + ESD & 58.8 & 58.7 & 57.9 & 56.4 & 55.1 & 52.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Accuracy comparison of the RAVDESS [29] test dataset for models with different training datasets. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Training Dataset**} & \multicolumn{6}{c}{**Accuracy (\%)**} \\ \cline{2-7}  & **Clean** & **20 dB** & **5 dB** & **0 dB** & \(-\)**3 dB** & \(-\)**6 dB** \\ \hline IEMOCAP & 55.2 & 55.8 & 57.4 & 58.8 & 59.8 & 59.7 \\ ESD * [31] & 69.3 & 69.5 & 67.7 & 66.9 & 66.0 & 64.0 \\ IEMOCAP + ESD & 75.2 & 75.7 & 75.3 & 73.9 & 73.0 & 71.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Accuracy comparison of the EmoDB [30] test dataset for models with different training datasets. input waveform. The emotion classifier generates an emotion probability vector of [4] from the emotion classifier input waveform. The six decoder blocks perform the denoising operation to generate a cleaned-up emotion classifier input waveform from a noisy speech waveform input. The six-decoder architecture reduces the number of model parameters to 2.8 M for inference from 4.2 M for training by turning off the five decoder blocks for the four band-pass filtered waveforms and the pitch-related waveform. The model is trained to fit the five decoder block outputs (four band-pass filtered waveforms, a pitch-related waveform) and an emotion probability vector to the ground-truth counterparts by using a loss function which is the sum of the wave loss function and the cross-entropy emotion loss function. Because of the normalized L1 loss function used for the wave loss function, the high-frequency details are well retained in the emotion classifier input waveform. The IEMOCAP [25] was used for the clean speech dataset.