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As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual… (More)

In this paper, we study the stability of two kinds of frames generated by nonlinear Fourier atoms. The first result is the Kadec type 1 4-theorem. The second states that the nonlinear windowed Fourier atoms form a frame of L 2 (R). 1 4-theorem; Weyl–Heisenberg frame.

This paper presents a new approach to represent face by using a non-tensor product bivariate wavelet filters. A new non-tensor product bivariate wavelet filter banks with linear phase are constructed from the centrally symmetric matrices. Our investigations demonstrate that these filter banks have a matrix factorization and they are capable of representing… (More)

A ladder shaped filter of two real parameters a 1 , a 2 ∈ (−1, 1) is introduced in this note. The impulse response of the corresponding Linear Time Invariant (LTI) system is a generalized Sinc function of two parameters. Consequently a generalized Shannon-type sampling theorem is established for a class of non-bandlimited signals with special spectrum… (More)

In many cases, a real-valued signal x(t) may be associated with a complex-valued signal a(t)e ~°(t) , the analytic signal associated with x'(t) with the characteristic properties x(t) = a(t) cos O(t) and "H(a(.)cos0(-))(t) = a(t)sin0(t). Using such obtained amplitude-frequency modulation the instantaneous frequency of x(t) at the time to may be defined to… (More)