Statistical Analysis of Two Polarity Detection Schemes in Speech Watermarking

Statistical Analysis of Two Polarity Detection Schemes in Speech Watermarking Bin Yan1, Zhe-Ming Lu1, Jeng-Shyang Pan2, Sheng-He Sun1 1Department of Automatic Test and Control, Harbin Institute of Technology, P. O. Box 339, 150001 Harbin, P. R. China. yanbinhit@hotmail.com zhemingl@yahoo.com 2Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan, R.O.C. jspan@cc.kuas.edu.tw Abstract Polarity inversion based speech watermarking scheme hide data in speech by modification of the speech polarity. This paper build a statistical model of the polarity detection problem, based on this model, the original polarity detection scheme and the optimal detection scheme are analyzed and compared. The theoretical analysis results are validated by Monte Carlo simulation, the optimal polarity detector shows significant performance gain compared with the original polarity detection algorithm. 1 Introduction Polarity Inversion (PI) based watermarking scheme utilizes the fact that the human auditory system (HAS) is insensitive to the polarity of the speech signal [1]. Secure data can be hidden in speech signal by inverting the polarity of certain portion of the signal. PI watermarking can be classified as phase coding scheme [2, 3], the phase of the speech is changed by 180 degrees for PI watermarking. PI is very robust against noise addition and filtering operations because the polarity of the voiced frame won’t change under these manipulations. The drawback of PI watermarking is that it is not secure, but it is very useful for content annotation and in-band signalling applications [4]. The problem to be solved by this paper is to evaluate the performance of the polarity detection algorithms. This is done by first building a statistical model for the speech residual signal, based on this model, the performance of the original polarity detection algorithm is analyzed, this result is compared to the performance of the optimal polarity detector. Finally, we perform Monte Carlo simulation to validate the theoretical analysis. 2 Detection Performance of the Original Method The polarity detection scheme proposed by [1] can be summarized as a two-step procedure for each syllable, first, the polarity of the maximum peak in the LPC residual signal of each voiced frame is estimated, second, the polarity of each syllable is determined by majority vote. In this section we will analyze the error probability of this detection scheme. When the AR model order is properly chosen, the residual signal of the voiced frame can be modeled as impulse train in Additive White Gaussian Noise (AWGN), so we can build the following model under each hypothesis: H0 : s[n] = − K−1 � k=0 Aδ[n − kP] + w[n] (1) H1 : s[n] = + K−1 � k=0 Aδ[n − kP] + w[n] , (2) where P is the pitch period, A is the amplitude of the impulse train, K is the number of pitch period in each frame, w[n] is Gaussian noise with mean zero and variance σ2. For ease of analysis, we made the following assumptions: the sample values in the location of impulses are not affected by the …

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