# Exploring the Effectiveness of the Phase Features on Double Compressed AMR Speech Detection
## 8 Discussion and Conclusions
Furthermore, alongside traditional LSTM networks, we proposed a parallel LSTM system for DC AMR speech detection. This parallel LSTM system simultaneously receives both spectrogram and phase spectrum as inputs and processes these features separately to learn the most representative deep features. Subsequently, the learned deep feature representations are concatenated to form a single feature vector, encompassing both magnitude and phase information. This concatenated feature vector is then applied to the fully connected (FC) and classification layers. Our goal with this approach was to investigate whether magnitude and phase spectra convey complementary information for the DC AMR speech detection task. Experiments conducted on the TIMIT database showed that CosPhase and DCT + CosPhase features yield as good performance as magnitude spectrum features on the AMR-NB codec (Table 1). For example, while the spectrogram feature gave a 99.98% true positive rate (TPR) for AMR-NB-coded DC speech signals, a TPR of 99.84% was obtained using CosPhase features. Conversely, for the AMR-WB codec, CosPhase features were found to be superior to the spectrogram features (86.51% vs. 80.06% TPR values) using the baseline LSTM-based classifier (Table 1). The superior performance of the CosPhase features was expected because the dynamic range of the unwrapped phase spectrum features exhibits large variations, which possibly makes it difficult to accurately model the phase information. However, applying the cosine function to the phase spectrum reduces the dynamic range of the features and normalizes them within the range \([-1,1]\). Hence, this helps the classifier learn the discriminative features more accurately. Utilizing the proposed parallel LSTM network using spectrogram and CosPhase features further improved the DC AMR-NB speech detection performance compared to the stand-alone CosPhase features with the baseline LSTM network. For example, stand-alone CosPhase features yielded a 100% TPR for only 9 out of the possible 64 BR1-BR2 combinations (Table 3), whereas the parallel LSTM system with spectrogram and CosPhase inputs achieved a perfect detection rate (100% TPR) in 45 BR1-BR2 cases (Table 4). This observation suggests that the CosPhase features convey complementary information to the spectrogram features; hence, fusing the learned deep features further improves the detection rates for the AMR-NB codec. Additionally, the computational speeds of the proposed baseline LSTM and parallel LSTM systems for processing a single trial (one input signal) were compared. It was found that the baseline LSTM system completesa prediction in 0.05 s, while the parallel LSTM system requires 0.07 s. The difference in computation time is expected since the parallel LSTM simultaneously propagates two input features (spectrogram and phase spectrum) through two distinct LSTM branches, thereby extending the prediction time. Nonetheless, the prediction times for both systems are relatively short, demonstrating that the proposed system is capable of operating in real time. Experimental results carried out using the AMR-WB codec showed that detecting DC AMR-WB speech signals is a more challenging task than detecting AMR-NB speech signals. The detection rates obtained using the AMR-WB codec (TNR or TPR values) were found to be considerably lower than those obtained using the AMR-NB codec. However, CosPhase features were found to be significantly superior to spectrogram features in detecting AMR-WB-coded speech signals. For instance, while a TPR value of 71.92% was obtained using spectrogram features when BR1 = 23.85 kbps and BR2 = 23.05 kbps (Table 5), CosPhase features brought approximately a 38% relative improvement, yielding a TPR value of 99.26% (Table 6). The use of both spectrogram and CosPhase features with parallel LSTM further improved SC (Figure 7) and DC AMR-WB speech detection (Table 7) performances independently of the compression bit rates.