## 5 Experiments  
### Audio Quality Evaluation  
To objectively assess audio quality, we employed two widely-used metrics: Signal-to-Noise Ratio (SNR), Segmental Signal-to-Noise Ratio (segSNR), and Perceptual Evaluation of Speech Quality (PESQ). The PESQ gives the Mean Opinion Score Listening Quality Objective (MOS-LQO) score, as defined in ITU-T Recommendation P.862.1 [47]. For these evaluations, we utilized AFsp version 9.0 for SNR and segSNR calculations and PESQ version 1.2 for MOS-LQO scores. Our experiments were conducted on the ITU-T Test Signals for Telecommunication Systems--Test Vectors Associated with the Rec. ITU-T P.50 Appendix I dataset. This dataset comprises 12 speech recordings (12 speakers across 6 languages: American English, Arabic, Mandarin Chinese, Danish, French, and German), with each recording featuring a monophonic waveform sampled at 16 kHz and quantized to 16 bits. We set the number of DCT coefficients per frame (\(N\)) for our experiments to 2048. We compared three alternative expansion strategies:  
1. **Fixed Expansion:** Expanding the top four blocks with the highest coefficients (our previous work). 2. **Random Expansion:** Randomly expanding four or five blocks from the top coefficients. 3. **Adaptive Expansion:** Expanding the top four blocks with the lowest estimated distortion, selected in ascending order. On expansion strategies, we explored several possibilities of hiding locations. Even for fixed locations for embedding, we tried to embed data into different locations and evaluated the audio quality in our previous work [5]. In each frame, 2048 coefficients are divided into 16 blocks. We expanded every eight blocks from the low-frequency (2 nd block) domain to the middle-frequency domain (9 th block) as the start blocks for expansion. We calculated segSNRs and MOS for expansion of the [2 nd, 9 th], [3 rd, 10 th], [4 th, 11 th], [5 th, 12 th], [6 th, 13 th], [7 th, 14 th], [8 th, 15 th], and [9 th, 16 th] blocks, and the expansion of [9 th,16 th] has the best MOS value 4.41 and the best segSNR 23.32 dB when capacity \(\approx\) 8000 bps. Furthermore, overflow did not occur out of 112 tracks when expanding the fixed [9 th,16 th] block. Thus, for fixed expansion, we chose coefficients from the highest-frequency domain in this paper as a reference for comparison. Figure 2 visually illustrates the different expansion patterns for each strategy. In Figure 2a, fixed expansion--a fixed pattern with a clear boundary. In Figure 2b, random expansion shows a less predictable pattern but still has a discernible boundary. In Figure 2c adaptive expansion shows a highly variable pattern, with different expansion locations for each frame, making it more resilient towards spectrum-based attacks. By comparing these patterns, it is evident that the adaptive expansion strategy Figure 2c offers the highest level of complexity, potentially making it more difficult for attackers to detect and exploit embedding patterns. Figure 3 presents the MOS, SNR, and segSNR values for the different expansion strategies. As with the MOS-LQO results, both the previous work and the proposed random expansion (solution 1) yield relatively high MOS-LQO scores. The adaptive expansion (solution 2) generally exhibits slightly lower scores, but all of the values remain above 4.085, indicating imperceptible distortion. As for the SNR, the adaptive expansion (solution 2) outperforms both the previous work and the random expansion (solution 1) in terms of SNR. Finally, in segSNR, solution 2 demonstrates superior segSNR performance compared to solution 1. Both proposed methods exhibit higher segSNR values than the previous work. The minimum segSNR value of the three methods is 21.363 dB, which indicates good audio quality. This also suggests that the time-domain differences between the stego and original data are smaller for the proposed methods. Figure 3: _Cont_.