## 5 Imperceptibility  
Imperceptibility is tool to measure the similarity or resemblance between signals. This is the most vital parameter in mimicry covert underwater acoustic communication. The main key of biologically inspired covert communication is the likeness of a man-made signal with real sea ocean noise [4]. The mimicked signal containing a watermark should be akin to the original ocean noise. When the eavesdropper detects the mimicked signal it should be identified as a cetacean vocal due to its resemblance in structure, time duration, intensity, frequency and modulation. The geographical location of a particular vocal should also be considered and covert experiments should be performed in the same particular region where the specific cetacean exists. The mimicked signal should be highly imperceptible with the real ocean noise waveform. There are a variety of methods to measure imperceptibility ofaudio vocals. Usually imperceptibility is measured through a human auditory system (HAS), time correlation and comparing the frequency spectrum [41; 42]. Correlation methods are usually used if any information is embedded in the audio signal. It checks the similarity between two signals by a cross correlation of waveforms. The higher  
Figure 11: Detection of “club” and calculation of time delay between elements. Figure 12: Extraction of mimicked information “COMMUNICATION” from the received signal. the value of correlation equates to higher imperceptibility. HAS is used to check imperceptibility by the response of users listening to the voice. It is done by making a mean score through a pool of people listening the voice. If the mean score is higher, then it is assumed that the voices are similar. Another method to check imperceptibility is by comparing the frequency spectrum of the original and mimicked signal. This is done by mapping the spectrum characteristics of the real and mimicked voice. If the sound holds the characteristics of a particular vocal, it is identified as the particular vocal. In this article, we opted to estimate imperceptibility by comparing the frequency spectrum. In this research, the covert information is watermarked by shuffling the humpback whale song segments. None of the ingredients other than the humpback whale song is added in the communication waveform, however the pattern of the humpback whale is altered. The humpback whale produces long duration songs with a variety of themes and patterns. Each theme is composed of phrases that repeat several times before a new theme. The exact pattern of the humpback whale song or repetition of phrases is unknown [43]. There is no evidence that humpback songs are hierarchically structured [35]. However they sing the song in the bandwidth of 8 kHz. New humpback whale songs are being discovered with new phrases and patterns [34]. This is similar to an English speaking singer singing the songs. He will sing a variety of songs but a listener will identify it all as English songs. Thus we can conclude that a humpback whale sings a variety of songs with diverse patterns within its bandwidth range and spectrum characteristics. To verify the variable patterns of a humpback whale song, several samples of humpback whale songs are compared. Figure 13 shows the spectrum characteristics of some phrases of different humpback whale songs depicted from the ocean acoustic library [36]. It is evident form the figure that humpback whale songs have diverse characteristics with various patterns but the bandwidth of the waveform lies within 8 kHz. The main energy in concentrated within 4 kHz. Thus we can conclude there is no fix pattern of humpback whale songs. Figure 13: Spectrum of multiple humpback whale songs’ segments. (**a–d**) shows the spectrum of four different Humpback whale songs. We can clearly notice that the frequency spectrum of all humpback whale songs are different and not identical which shows that they don’t have any regular pattern.