 # A Fast and Precise Synchronization Method for Digital Audio Watermarking

DOI: 10.4018/978-1-61520-925-5.ch012

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## 12.2 The Synchronization Problem In Watermarking And Traditional Solutions

In this section, the synchronization problem in audio watermarking is illustrated first followed by the traditional solutions.

### 12.2.1 Synchronization Problem in Audio Watermarking

Due to the similarities between watermarking and communication, the watermarking channel is usually modeled as a conventional communication channel (Cox et al., 2002) as shown in Figure 1.

Suppose the message to be transmitted is m, which is usually modulated to the watermark w and the cover signal is x, then the watermarked signal s iss = x + aw(12.1) where a is a factor between 0 and 1 controlling watermark strength to prevent introducing perceptible distortion.

There are two types of detectors at the watermark detection side, blind detector where the original host signal is not available for detection, and informed detector, where the host signal is accessible during the detection phase, as indicated by the broken box and arrows in Figure 1. Correlation between received signal and the watermark is performed and a high value of the correlation denotes the existence of watermark. Suppose the length of watermark is N and the channel noise introduced during the transmission is n, then the received signal r isr = s + n = x + aw +n(12.2) and the correlation between r and w is

(12.3)

Assuming N is sufficiently large, watermark w, host signal x and noise n are independent and Gaussian distributed. Then

(12.4)

The optimized threshold for watermark detection is chosen as

(12.5)

There are two detection errors that occur, namely false positive error and false negative error. The former denotes the situation when the detector claims the existence of a watermark in an un-watermarked signal section and the latter denotes the opposite. Suppose the probability for false positive and false negative are Pfp and Pfn respectively and the threshold is chosen as in Equation (12.5), then (Kim, 2003)

(12.6) where σr is the standard deviation of the received signal r and erfc() is the complementary error function defined as

(12.7)

During the recovery process, the detector needs to know the starting location of the watermark in the received signal. This brings up the synchronization issue. The above Equation (12.3) holds only when the received signal is perfectly aligned with the watermark, in other words, when signal r is synchronized with watermark w, correlation c will reach its maximum. A typical result of c is illustrated in Figure 2. Note in Figure 2, the location of the peak is the beginning of the embedded watermark.

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