# Exploring the Effectiveness of the Phase Features on Double Compressed AMR Speech Detection
## 8 Discussion and Conclusions  
In this study, we investigated phase-spectrum-based features for DC AMR narrowband (AMR-NB) and wideband (AMR-WB) speech detection. To the best of our knowledge, this is the first study to utilize phase spectrum features for DC audio or speech detection tasks. We demonstrated that compressing a speech signal for the first time using the AMR-NB codec significantly affects phase spectrum components above 500 Hz compared to the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & \multicolumn{5}{c}{BR2 (kbps)} \\  & & 6.6 & 8.85 & 12.65 & 14.25 & 15.85 & 18.25 & 19.85 & 23.05 & 23.85 \\ \hline  & 6.6 & 73.78 & 74.64 & 91.31 & 93.70 & 93.76 & **96.33** & **97.30** & **98.26** & 93.61 \\  & 8.85 & 77.09 & 75.56 & 93.64 & **94.89** & 95.85 & 97.55 & 98.47 & 98.99 & **96.21** \\  & 12.65 & 75.04 & 73.01 & **90.96** & 93.30 & 93.43 & 96.08 & 97.11 & 98.45 & **94.64** \\  & 14.25 & 75.89 & 73.32 & **91.29** & 93.05 & 93.20 & 96.56 & 97.19 & 98.80 & 94.49 \\ BR1 & 15.85 & 76.31 & 74.47 & **91.61** & **94.03** & 93.36 & 96.50 & 97.25 & 98.84 & 94.84 \\ (kbps) & 18.25 & 76.19 & 73.53 & **92.57** & 93.99 & 94.58 & 96.56 & 97.23 & 98.74 & 94.70 \\  & 19.85 & 76.42 & 75.64 & **91.48** & 93.24 & 93.70 & 96.86 & 97.28 & 98.68 & 94.81 \\  & 23.05 & 77.40 & 75.12 & **93.26** & 94.72 & 94.74 & 96.88 & 97.63 & 98.93 & 95.31 \\  & 23.85 & 79.45 & **79.79** & **91.86** & **94.16** & 93.95 & 96.90 & 98.03 & 99.22 & 95.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: TPR detection rates (in %) for DC AMR-WB speech utilizing spectrogram and CosPhase features with the proposed parallel LSTM network. Underlined entries indicate conditions where the parallel LSTM outperforms the baseline LSTM system with CosPhase features (Table 6), whereas bold numbers indicate cases where the parallel LSTM is superior to the baseline LSTM system with spectrogram features (Table 5). Figure 7: Detection rates (TNR in %) for SC AMR-WB speech obtained using the baseline LSTM system with spectrogram and CosPhase features and the proposed parallel LSTM system. uncompressed (original) signal. Additionally, SC speech signals compressed at different bit rates exhibit distinct phase spectra (left panel of Figure 2). Similarly, we observed differences in phase spectra of DC narrowband speech signals at higher frequencies (right panel of Figure 2). Likewise, phase spectra of SC AMR-WB speech signals differ from the original speech signal, and compressing the speech signals for the second time has a considerable impact on the phase spectrum compared to the SC speech spectrum (Figure 3). Based on these observations, it is evident that the phase spectrum can serve as a discriminative feature to distinguish SC and DC-AMR-coded speech signals for both AMR-NB and AMR-WB codecs. We proposed three different phase spectrum-based feature representations for DC AMR speech detection: (i) conventional STFT phase spectrum, where the unwrapped phase spectrum of the STFT of the speech signal was used as the features; (ii) CosPhase features, where cosine normalization was applied to the unwrapped phase spectrum to reduce the dynamic range of the features; and (iii) DCT + CosPhase features, where discrete cosine transform was applied to the cosine normalized features to obtain uncorrelated feature representations. The magnitude spectrum (spectrogram) was also used as the baseline feature to compare the performance of the proposed phase spectrum features. In addition to proposing phase-spectrum-based features for DC AMR speech detection, we introduced a novel DNN-based classification system based on LSTM networks. LSTM networks are renowned for their exceptional performance on time-series data, and since both the spectrograms and phase spectra serve as time-series representations of magnitude and phase information, respectively, we utilized LSTM networks for DC AMR detection. To the best of our knowledge, this is the first study to propose the use of LSTM networks for DC audio detection.