# Exploring the Effectiveness of the Phase Features on Double Compressed AMR Speech Detection
## 7 Experimental Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Input**} & \multicolumn{2}{c}{**AMR-NB**} & \multicolumn{2}{c}{**AMR-WB**} \\ \cline{2-5}  & **TNR (\%)** & **TPR (\%)** & **TNR (\%)** & **TPR (\%)** \\ \hline Spectrogram & 99.94 & 99.98 & 76.73 & 80.06 \\ Phase Spectrum & 83.40 & 81.82 & 68.65 & 62.46 \\ CosPhase & 99.93 & 99.84 & 84.03 & 86.51 \\ DCT + CosPhase & 98.72 & 97.95 & 57.47 & 42.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average TNR and TPR values for AMR-NB and AMR-WB codecs obtained using different feature representations and the baseline LSTM system The DC AMR-NB detection rates obtained using the proposed CosPhase features and the baseline LSTM system for each possible BR1-BR2 combination are reported in Table 3. The results summarized in the table demonstrate the effectiveness of phase spectrum features in detecting DC AMR-NB speech signals. Nearly all of the detection rates reported in the table (except for three entries) exceed 99.5%, indicating the efficacy of the proposed features. The lowest detection rate (98.82%) is observed when BR1 = 12.2 kbps and BR2 = 4.75 kbps, corresponding to a radical down-transcoding procedure. We next investigate the impact of combining information learned from spectrogram and CosPhase features using the proposed parallel LSTM network structure outlined in Section 5. Figure 6 illustrates the SC AMR-NB detection rates (TNR values) obtained using the parallel LSTM system, along with the results obtained using single features with the baseline LSTM system for comparison. From the figure, it is evident that the parallel LSTM system outperforms stand-alone spectrogram or phase spectrum features in most cases. However, it is noteworthy that the TNR values depicted in the figure are very close to each other, making it challenging to draw a general conclusion solely based on the TNR values. Hence, the DC AMR-NB speech detection rates obtained using the parallel LSTM system are reported in Table 4. Notably, perfect detection rates (100%) are observed for the majority of BR1-BR2 cases. Comparing the detection rates in the table with the results obtained using stand-alone CosPhase features given in Table 3, it is evident that phase spectrum and spectrogram features complement each other. Consequently, combining the learned deep features from the spectrogram and CosPhase features through parallel LSTM further enhances the detection rates for the AMR-NB codec. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature** & **System** & **BR1 (kbps)** & **BR2 (kbps)** & **TPR** \\ \hline Spectrogram & LSTM & 4.75 & 4.75 & 99.47 \\ Spectrogram & LSTM & 4.75 & 5.9 & 99.94 \\ Spectrogram & LSTM & 4.75 & 6.7 & 99.83 \\ Spectrogram & LSTM & 4.75 & 7.95 & 99.80 \\ Spectrogram & LSTM & 4.75 & 10.2 & 99.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detection rates (TPR in %) for DC AMR-NB speech using spectrogram features and the baseline LSTM network. BR1: first compression bit rate and BR2: second compression bit rate. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & \multicolumn{5}{c}{BR2 (kbps)} \\  & & 4.75 & 5.15 & 5.9 & 6.7 & 7.4 & 7.95 & 10.2 & 12.2 \\ \hline  & 4.75 & 99.89 & 99.83 & 99.39 & 99.20 & 99.97  
In the experiments, we next explore the impact of phase features on DC AMR-WB speech detection. The DC AMR-WB speech detection rates obtained using individual spectrogram and CosPhase features with the baseline LSTM network are summarized in Tables 5 and 6, respectively. The detection rates where CosPhase features are superior to the spectrogram features are underlined in Table 6 for ease of comparison. Firstly, one can observe that unlike the AMR-NB codec (Tables 2 and 3), where the detection rates are consistently higher than 99.5%, DC AMR-WB detection rates are notably lower regardless of the features. This confirms that DC AMR-WB speech detection is indeed a more challenging task compared to detecting DC AMR-NB speech.