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Audio Watermarking through Parametric Signal Representations

Yi-Wen Liu

advised by: Prof. Julius Smith

Center for Computer Research in Music and Acoustics
Stanford University, Stanford, CA 94305, USA

Synthesized multimedia objects are emerging everywhere now. One can talk on the phone to a virtual representative that speaks a synthesized tongue, drink soda of synthesized taste, such as Coke, or even fall in love with a synthesized graphic character. It becomes urgent to protect such objects as intelectual properties, for the synthesis of them often involves a lot of computation power and human labor. In my dissertation research, a framework is proposed for the design of robust watermarking algorithms on the synthesis parameter domain.   Particularly for audio signals that are sinusoidal in nature, such as vowels of human speech or sustaining tones of a musical instrument, I have been experimenting the idea of watermarking by quantizing the frequency. To implement it, a signal has to first be decomposed into sinusoidal and non-sinusoidal components.  Then, frequencies of sinusoidal partials are quantized to carry binary information. The quantization is set to be as small as can not be heard by human ears, but meanwhile as large as possible so that the quantization step can easily be resolved when the watermark's binary information needs to be extracted.  The frequency-quantized sinusoids are carefully synthesized and superposed with the non-sinusoidal components, which are un-altered, to form a watermarked version of the original signal.

To decode the watermark embedded as described above, a frequency estimator with very high accuracy is necessary.  I developed an efficient algorithm that can track 50-100 partials from a mildly noisy observation.  The algorithm often (but not always) approaches the Cramer-Rao lower bound, a theoretical limit in parameter estimation.  Empirically, the algorithm works well when all partials in the spectrum are well separated to begin with.

A somewhat disjoint branch of my dissertation research in on the theory side.  I am interested in the modeling of watermarking as what is called "writing on dirty paper" (WDP).  In particular, I am interested in studying Shannon's data hiding limits on transimitting multiple watermarks to a common host at multiple rates.  I call it "broadcast on dirty paper" (BDP), and demonstrated that the data hiding capacity region is larger if one considers power-sharing rather than time-sharing for embedding multiple watermarks.  Preliminary simulations on joint "spread-spectrum" and "quantization" watermarking also support the power-sharing scheme.

Yi-Wen Liu, 3/16/2005