## 4 Results and Discussion
### Subjective Tests and Investigation on the Effects of Non-Linear Distortions of Real Speakers  
Subjective tests were conducted in two parts. In the first part, an audio signal with a duration of five seconds was generated as explained onwards: the ticking sounds, used also in the other experiments of the paper, available at [41], were processed according to the watermark generation procedure described in the paper, using five randomly selected ENF values from the variation over one year made available by [6]. The ticking sound to chirp signals power ratio was set to 20 dB, resulting the sonic watermark. A random vocal signal from the database available at [43] was selected. The sonic watermark was summed with the vocal signal. The power ratio between the vocal signal and the sonic watermark was set to 6 dB. It can be observed that the power ratio values that gave the best results in the watermark recovery were selected for this test. The signal was presented to 60 listeners and they were asked to describe what they hear. None of the listeners mentioned that the ticking  
Figure 18: The probability of occurrence of a certain number, between 3 and 6, consecutive equal ENF values in one year, if the ENF values are captured every second.  
sound is suspicious. Most of the listeners wrote the words that were said in the recording mentioning the ticking of a clock in background. Some of them described the recording as: \"I hear a man speaking and the ticking of a clock in the background.\" The second part was a blind test: the same 60 listeners were presented with two audio signals one after the other. The first signal was 5 s long, containing the sonic watermark (ticking sounds summed with the chirp signals, the power ratio between the ticking sounds and the chirp signals being the same as in the first experiment, 20 dB) and no vocal signal. The only difference between this first signal and the second one was that the latter did not contain the chirp signals (it only contained the ticking sounds). The following question was asked: \"Are the two signals identical?\" The available answers were \"Yes\" and \"No\". If the listeners answered \"No\", they were asked what is different between the two signals. Only six listeners described the first signal as having more high frequency content than the latter, thus it can be concluded that in 90% of the cases, the sonic watermark will not be detected, even with a reference signal available, and in 100% of the cases the sonic watermark will not draw attention to it if no reference signal is available. From the 60 listeners, 25 used headphones during the test, 22 used laptop speakers, eight used smartphone speakers and five declared that they used \"speakers\" without declaring a type. This is a very tough test because, in real scenarios, the listeners would not have available the unmodified ticking sounds for comparison. The test returned very good results.  
To determine the effects of the non-linear distortions of real speakers on the chirp signals detection, experiments were conducted in three situations, using the following speakers: professional audio monitor speakers (Samson Media One M50), budget speakers (Genius SP-U120), and laptop speakers (ASUS ROG GL753 VD). In every case, 10 signals were played, every signal with a duration of five seconds, containing a sum of chirp signals encoding five random values of ENF, generated according to the method presented in the paper. The sound recording device was a Samsung Galaxy S10 smartphone. In all the cases, we determined 100% correct detection. From these experiments it results that the speakers' non-linear distortions do not have degrading effects on the detection of the chirp signals in the situation presented in the paper.