# Exploring the Effectiveness of the Phase Features on Double Compressed AMR Speech Detection
## 7 Experimental Results
For spectrogram features, when the first compression bitrate (BR1) is fixed, DC speech detection rates generally decrease as the BR2 value increases. Similarly, a similar observation is noted when BR1 increases for a fixed value of BR2. Regarding the CosPhase features, higher detection rates are observed as BR1 (or BR2) increases for a fixed value of BR2 (or BR1). Upon comparing the results obtained using the magnitude spectrum (Table 5) and phase spectrum (Table 6), it becomes evident that in most cases, CosPhase features exhibit superior performance to spectrogram features. For instance, while a TPR value of 71.46% is obtained using spectrogram features when BR1 = 23.85 kbps and BR2 = 18.25 kbps, a considerable relative improvement of approximately 35% is observed using CosPhase features, yielding a TPR value of 96.82%. Similarly, when BR1 = 23.85 kbps and BR2 = 23.05 kbps, CosPhase features yield approximately 38% higher detection rates than spectrogram features. The results summarized in Tables 5 and 6 underscore the considerable impact of phase spectrum features on AMR-WB-coded speech detection, significantly enhancing DC speech detection performance compared to magnitude spectrum features. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \multicolumn{6}{c}{BR2 (kbps)} \\  & & 4.75 & 5.15 & 5.9 & 6.7 & 7.4 & 7.95 & 10.2 & 12.2 \\ \hline \multirow{8}{*}{BR1 (kbps)} & 4.75 & 99.42 & 99.83 & 99.75 & 99.26 & 99.80 & 99.58 & 99.83 & 99.80 \\  & 5.15 & 100 & 100 & 100 & 100 & 100 & 100 & 100 \\  & 5.95 & 100 & 100 & 100 & 100 & 100 & 100 & 100 \\  & 6.7 & 100 & 100 & 99.97 & 100 & 100 & 100 & 100 \\  & 7.4 & 100 & 100 & 99.94 & 100 & 100 & 100 & 100 \\  & 7.95 & 100 & 100 & 99.97 & 100 & 100 & 99.97 & 100 & 100 \\  & 10.2 & 100 & 99.89 & 100 & 100 & 100 & 100 & 100 & 100 \\  & 12.2 & 100 & 99.97 & 100 & 99.97 & 99.94 & 99.94 & 99.97 & 99.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: TPR detection rates (in %) for DC AMR-NB speech utilizing spectrogram and CosPhase features with the proposed parallel LSTM network. Figure 6: Detection rates (TNR in %) for SC AMR-NB compressed speech obtained using the baseline LSTM system with spectrogram and CosPhase features and the proposed parallel LSTM system. Finally, we investigate the performance of combining deep features learned through the proposed parallel LSTM system on AMR-WB-coded speech signals. The SC AMR-WB speech detection rates obtained using the parallel LSTM system are shown in Figure 7. Additionally, the TNR values obtained using spectrogram and CosPhase spectrum features with the baseline LSTM system are depicted in the figure to facilitate comparison between the proposed parallel system and the baseline system. It is evident from the figure that the parallel LSTM system outperforms the stand-alone systems regardless of the compression bit rate value. Similarly, CosPhase features yield higher TNR values than spectrogram features, irrespective of the bit rate. These two important observations suggest that (i) phase spectrum features are more representative than magnitude spectrum features for detecting SC AMR-WB speech, and (ii) phase spectrum features and spectrogram features convey complementary information. Combining the deep embeddings learned from these two features through the proposed parallel LSTM network further enhances SC AMR-WB speech detection. The DC AMR-WB speech detection rates obtained using the proposed parallel LSTM system for each BR1-BR2 combination are summarized in Table 7. In the table, underlined entries indicate BR1-BR2 combinations where the parallel LSTM outperforms the baseline LSTM system with CosPhase features (Table 6), while bold numbers highlight cases where the parallel LSTM yields higher detection rates than the baseline LSTM system with spectrogram features (Table 5).