## 4 Experimental Results And Analysis
### Analysis with Perceptual and Non-Perceptual Manipulations  
Once the hash codes of different recordings have been analyzed theoretically and experimentally, the next step is to examine the hash codes after applying perceptual and non-perceptual manipulations. The first ones preserve the content, i.e., that do not change the perceived content. Generally speaking, two audio clips can be considered significantly similar if they sound the same [38]. For forensics purposes, it is desirable that perceptually similar recordings have very similar hashes (i.e., a BER close to 0), while for non-perceptual manipulated recordings they have dissimilar hashes (i.e., a BER close to 50%). In order to illustrate BER values for perceptual and non-perceptual manipulations, we apply the following tests: FLAC, MPEG4 AAC, volume, re-sampling and re-quantization (perceptual), and LPF, additive noise, cutting and copy-move (non-perceptual). Table 4 describes the parameters used in each case. To illustrate an example, the signal shown in Figure 3(a) was used. In the case of perceptual manipulations, both the RMS (root mean squared) value of original minus modified signal, and the BER between the hash of the modified signal and the hash of the original signal were calculated (see Tables 5 and 6, respectively). According to these results, although RMS values can be higher than zero for perceptual manipulations, their BER values are lower than 11%. On the other hand, Figure 4 shows examples of non-perceptual manipulations, with BER values higher than 38%. This means that the hash values of signals with perceptual manipulations are similar to the hash value of the original signal, whereas for signals with non-perceptual manipulations, the hash values differ greatly from the original hash value. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Perceptual Manipulation** & **Description** & **Parameters** \\ \hline Format conversion: FLAC & Conversion to FLAC and returned to wav & Sample rate: 8 kHz \\ \hline Format conversion: MPEG-4 AAC and returned to wav & & \\ \hline Decrease Volume & The amplitude of the recording is attenuated by a scale of 2 & Gain: \(-6\) dB \\ \hline Re-sampling & Sampling frequency is set to 16 kHz and returned to 8 kHz & 8 kHz \(\rightarrow\) 16 kHz \(\rightarrow\) 8 kHz (using anti-aliasing FIR filter) \\ \hline Re-quantization & Each sample is quantized to 32 bits/sample, and returned to 16 bits/sample & 16 bits \(\rightarrow\) 32 bits \(\rightarrow\) 16 bits \\ \hline Low-pass filtering & Butterworth low pass filter (LPF) & 3 kHz, fifth order \\ \hline Noise & Gaussian Additive noise & \(\mu=0\,\sigma=0.01\) \\ \hline Cutting & Delete samples from the original signal & 5000 samples are deleted \\ \hline Copy-move & Copy and move samples in the original signal & 10,000 samples are exchanged \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Manipulations used to test perceptual and non-perceptual hashing. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Type** & **Theoretical Values** & **Experimental Values** \\ \hline Parameter & \(\mu_{t}\) & \(\sigma_{t}\) & \(\mu_{e}\) & \(\sigma_{e}\) \\ Value & 0.5 & 0.05103 & 0.4175 & 0.05439 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Expected values (\(t\)) and experimental values (\(e\)) obtained from the entire 124,750 BER values. \begin{table}
\begin{tabular}{c c} \hline \hline
**Signal** & **BER** \\ \hline Original & 0\% \\ Flac & 0\% \\ MPEG-4 AAC & 10.42\% \\ Volume & 4.17\% \\ Re-sampling & 1.04\% \\ Re-quantization & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Example of perceptual manipulations for original signal shown in Figure 3(a): BER values of original signal versus modified signal. Figure 4: Examples of non-perceptual manipulations and BER value between the hash of the original signal and the hash of the modified signal.