# Exploring the Effectiveness of the Phase Features on Double Compressed AMR Speech Detection
## 7 Experimental Results  
In the experiments, we initially assess the performance of individual feature representations using the baseline LSTM system for AMR-NB and AMR-WB speech detection. The average SC and DC detection rates (represented by TNR and TPR values, respectively) for each feature representation are summarized in Table 1. For each feature, the average SC detection rates are computed by averaging eight TNR values for the AMR-NB codec (8 BRvalues) and nine TNR values for the AMR-WB codec (9 BR values), respectively. Similarly, the average DC detection rates (TPR) are determined by aggregating 64 TPR values for the AMR-NB codec (8 BR1 \(\times\) 8 BR2 = 64 combinations) and 81 TPR values for the AMR-WB codec (9 BR1 \(\times\) 9 BR2 = 81 combinations), respectively. The results presented in the table reveal considerably higher detection rates achieved using the AMR-NB codec compared to the AMR-WB encoder, regardless of the feature set used. For instance, while the magnitude spectrum (spectrogram) features yield a 99.94% SC detection rate with the AMR-NB codec, it reduces to 76.73% for the AMR-WB codec. Similarly, employing spectrogram features results in a TPR value of 99.98% with the AMR-NB codec, whereas a degradation of approximately 20% is observed in the DC detection rate (TPR of 80.06%) when utilizing the AMR-WB codec. This trend persists for the phase spectrum features as well, indicating that detecting AMR-WB-coded speech signals is inherently more challenging than detecting narrowband signals, regardless of the feature representation employed. An important observation from the table is that, for narrowband AMR-coded speech signals, the proposed phase-spectrum-based features (except the raw phase spectrum) yield comparable results to spectrogram features. For instance, while spectrogram features achieve a 99.94% average SC detection rate, CosPhase and DCT+CosPhase features yield average TNR values of 99.93% and 98.72%, respectively. Similarly, the TPR values obtained using CosPhase features and DCT + CosPhase features closely match the DC AMR-NB detection rate of spectrogram features. For wideband-coded speech signals, CosPhase features exhibit higher detection rates compared to spectrogram features for both SC and DC speech signals. For instance, while spectrogram features achieve 76.73% and 80.06% average TNR and TPR values, respectively, CosPhase features further enhance the SC and DC detection rates to 84.03% (approximately 10% relative improvement) and 86.51% (approximately 8% relative improvement), respectively. The elevated detection rates achieved using phase spectrum features on both AMR-NB and AMR-WB compressed speech signal detection indicate that phase spectrum conveys useful information for DC speech detection. Among the three proposed phase-spectrum-based features, CosPhase features yield the highest detection rates for both SC and DC speech signals, regardless of the codec. Therefore, CosPhase features will be utilized in the remaining experiments. To further analyze the DC detection rates obtained using spectrogram and CosPhase features, we present the TPR values for each combination of first and second compression bit rates (BR1-BR2). Table 2 summarizes the TPR values obtained using spectrogram features and the baseline LSTM system on the AMR-NB codec. Although there are 64 possible combinations of BR1-BR2 pairs for DC AMR-NB-coded speech signals, only 6 cases yield TPR values lower than 100%. Hence, in Table 2, bit rate combinations that provide 100% detection rates are omitted for clarity. Interestingly, among these six BR1-BR2 combinations where detection rates are lower than 100%, the BR1 value is consistently 4.75 kbps, and as the BR2 value increases, the detection rate slightly decreases in general. However, the reduction in detection rates is negligible.