# Synchronization of Acoustic Signals for Steganographic Transmission
## 4 Technique Development and Implementation
### Monotonic Phase Correction  
The synchronizing signal synthesis system is shown in Figure 1. The input signal here is a Stego Object (signal in which steganographic information is embedded). The \(SMR(k)\) masking curve was determined based on the psychoacoustic model of the MPEG-1 standard [46] according to the procedure described in [48]. For each frame and  
Figure 1: Block diagram of the synchronizing signal synthesis system for the MPC method. each harmonic component, the value of the correction factor was determined in accordance with the relationship. \[SMR_{i}(k)=SPL_{i}(k)-LT_{i}^{\text{min}}(k)+C_{i}, \tag{1}\]  
where:  
\(i\)--signal frame number,  
\(k\)--harmonic number,  
\(SPL_{i}(k)\)--sound pressure level for the \(i\)-th original signal frame,  
\(LT_{i}^{\text{min}}\)--the minimum masking threshold for the \(i\)-th original signal frame,  
\(C_{i}\)--additional optional correction factor. In an OFDM (Orthogonal Frequency Division Multiplexing) block, a signal is formed which is the sum of 14 harmonic components. The OFDM signal is contained in the band from 375 Hz to 500 Hz and from 3041.7 Hz to 3166.7 Hz. Figure 2 shows a single OFDM signal frame and the corresponding amplitude spectrum. The OFDM signal frame duration is 48 ms. The OFDM signal phase is set as follows:  
\[\varphi(k)=\left\{ \begin{array}{cc}0,&k=\{1,4,7,8,11,14\},&\text{ pilots harmonics}\\ \frac{\pi}{2},&k=\{2,3,5,6,9,10,12,13\}&\text{synchronization harmonics}\end{array} ,\right. \tag{2}\]  
Figure 3 shows the synchronization system. The input signal \(x^{s,syn}(n)\) is fed first to the input of the phase angle scanner system. The task of the phase angle scanner is to determine the value of the phase angle jitter [49; 50]. This jitter may arise as a result of different accuracy of the clocks that clock the sampling circuits in the steganographic signal transmitter and receiver. The next stage of the synchronizing system operation is the detection of pilot spectral lines. This procedure consists of checking whether a given pilot spectral line, after correcting its phase angle by the value of the determined jitter correction, has a phase angle value of zero. If the number of pilot spectral lines thus detected is greater than or equal to 4, then the input is assumed to be a steganographic signal and the algorithm moves to the timing step. Figure 2: OFDM signal frame in time (upper picture) and frequency (amplitude spectrum, lower picture). The time synchronization mechanism is based on the analysis of the cumulative phase of the signal. The cumulative phase is determined based on the recursive equation:  
\[\chi_{1,k}=0\] \[\chi_{i,k}=\chi_{i-1,k}+\varphi_{i-1,k}\quad i\geq 2, \tag{3}\]  
where:  
\(i\)--number of the analyzed signal frame,  
\(k\)--harmonic number of the synchronization spectral line, the constant component has the index \(k=0\),  
\(\varphi_{i,k}\)--value of the phase angle of the \(k\)-th harmonic in the \(i\)-th frame. Figures 4 and 5 show the cumulative phase waveform for an exemplary steganographic signal, in which a synchronizing signal was additionally embedded. The continuous line marks the course of the cumulative phase of the signal on the transmitting side (in the synthesis circuit), and the dashed lines mark the courses of the cumulative phases recorded on the receiving side (in the synchronizer circuit). Figure 4 shows the cumulative waveforms of the signal in the absence of synchronization, and in Figure 5, when the synchronization is achieved. It is worth adding that for the presented characteristics, the average ratio of the steganographic signal energy to the energy of the synchronizing signal expressed in dB and determined in terms of segments (for 5 ms fragments) was 21.62 dB. Figure 4: Cumulative signal phase, no synchronization. Figure 3: Block diagram of the synchronization system for the MPC method.