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This paper describes a novel technique for embedding watermark bits into digital audio signals. The proposed method is based on the patchwork algorithm on the wavelet domain and does not need the original audio signal in the watermark detection. It uses the wavelet transform generated by the low-pass analysis filter h n whose length is 2 and h 0 = h 1 = 1(More)
One of the important capabilities for a subdivision scheme is the reproducing property of circular shapes or parts of conics that are important analytical shapes in geometrical modelling. In this regards, the first goal of this study is to provide necessary and sufficient conditions for a non-stationary subdivision to have the reproducing property of(More)
We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Ga-bor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal(More)
We analyze the internal structure of the multiresolution analyses of L 2 (R d) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V 0 to be the closed linear span of the shifts of the scaling function and W 0 that of the shifts of the wavelets. Finally, define V 1 to be the(More)