Cepstral Analysis for the Application of Echo-Based Audio Watermark Detection

Cepstral analysis is an important signal processing procedure for audio watermark detection in echo-based audio watermarking systems. However, with the use of two common versions, i.e., complex and real cepstra, this procedure is usually treated as a very standard routine. This paper starts from noting inappropriate cepstral analysis from existing works, and provides rigorous derivations to reveal the advantages of using real cepstrum than complex cepstrum in echo-based audio watermark detection. Furthermore, we introduce two alternatives, termed as real part and imaginary part cepstrum, respectively, based on which a joint detection scheme is proposed. This is achieved by noting that both real part and imaginary part cepstra contain a full version of the echo kernel coefficients, which can be appropriately combined to obtain a composite cepstrum to further suppress the interferences. The advantages of the joint detection scheme over conventional approach using real cepstrum are illustrated via both performance analysis and experimental results. The accuracies of the mathematical approximations for each version of cepstrum are evaluated by normalized misalignment. The detection robustness is evaluated using the peak-to-average power ratio. The relationships among echo length, echo delays, and scaling factor, during watermark detection phase, are also discussed. Experimental results of watermark detection rate are provided to compare the performance of complex, real, and composite cepstra, respectively.