## 4 Results and Discussion
### The Performance of Detecting Cut Operations  
The second experiment investigated the probability of detecting cut operations. For cuts that are longer than one second, the method presented in Section 3.4.1 is used. A prerequisite to this is to accurately determine the moment of recording. If the moment of the recording is not precisely detected, the cut operation cannot be identified, because, according to the method, the cut is searched around the detected moment. In the experiment, vocal signals [43] were concatenated, if necessary, to obtain the desired recording length. The recording length was varied between 1 and 20 min. The sonic watermark was synthesized, by using a randomly selected part of the ENF variation, equal to the necessary number of seconds, from the variation over one year [6]. The acoustic conditions were the following: meeting room environment, 6 dB vocal signal to sonic watermark PR, and 20 dB ticking sounds to chirp signals PR. Before extracting the ENF, a randomly positioned cut operation with a random duration between 2 and 20 s was executed on the signal. Based on the extracted ENF, the recording moment was determined, then the cut starting moment and duration were estimated and compared with the reference ones. Three possible results are obtained: the cut operation is not detected, is partially detected or perfectly detected. Partially detected means that the recording moment was correctly detected, but the cut start moment was not perfectly estimated. For each recording length, 100 experimental runs were done. The results are shown in Figure 17.  
Partially detecting the cut operation is caused by the existence of equal consecutive values in the ENF variation. This phenomenon is easier to explain using an example. Let us consider the reference ENF variation for an 8 s long recording to be \(A\), \(B\), \(C\), \(D\), \(D\), \(E\), \(F\), \(G\), where \(\overline{A,G}\) are values of the ENF. If the cut operation is one second long, done in one of the intervals where the \(D\) value is present, the extracted ENF variation would be \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), no matter if the part containing the first or the  
Figure 17: The performance of detecting a cut operation, depending on the length of the recording. second \(D\) value was removed. Therefore, an uncertainty of the cut start moment exists, but given the random variation of the ENF, these situations are rare. The probability of occurrence of several equal consecutive ENF values in a year, if ENF values are captured every second, is shown in Figure 18.  
From the results presented in Figure 17 it can be determined that the method gives good results for recording lengths of over 10 min, completely avoiding the wrong identification of the recording moment. The identification of cut operations smaller than one second is determined by the watermark extraction performance. If the watermark is extracted perfectly, then the detection rate is 100%. From the presented results, it can be determined that the proposed method is suitable for watermarking audio recordings of dialogues. The power ratio between the vocal signal and the sonic watermark should be kept at less or equal than 6 dB for best results. The sonic watermark should be synthesized so that the power ratio between the ticking sounds and the chirp signals is 20 dB. Thanks to the proposed auditory masking techniques, this value does not affect the auditory masking of the chirp signal by the ticking sounds. The recording duration plays an important role in determining the moment of the recording. The moment of a watermarked recording with a duration of at least 10 min can be precisely identified within a year period using the RSE and not the cross-correlation.