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Frame theory plays an important role in signal processing, image processing, data compression and sampling theory. In this short paper, some properties of Bessel sequences in Hilbert spaces are obtained, which generalize the existing results of frame to the case of Bessel sequences.
In this paper, the unified condition for stability of g-frames is established, and it is shown that the obtained results cover the existing results. The stability of g-Riesz bases is also established.
In this note, a necessary condition of multiwavelet frame in L2(R2) is given. Our result generalizes the result of existing univariate and single generator to the cases of 2-dimension with an arbitrary expansive matrix dilation and several generators.
The 3-band symmetric cardinal orthogonal scaling function with compact support is of interest in several applications. In this paper, we provide some characterizations of the 3-band symmetric cardinal orthogonal scaling function. We generalize some results of the symmetric cardinal orthogonal scaling function from the 2-band case to the 3-band case. Also, we find some new results.
The 3-band cardinal orthogonal scaling function with compact support is of interest in several applications such as sampling theory, signal processing, computer graphics. In this paper, We generalize some results of the cardinal orthogonal scaling function from the 2-band case to the 3-band case. We give the characterization. Also,we give some examples to prove our theory.
In this paper, we derive that there is a relation between the lowpass filter coefficient and wavelet’s samples in its integer points when a scaling function is a cardinal orthogonal scaling function. And we give some examples in which the lowpass filter coefficients are constructed from the wavelets. Then, we discuss the symmetry property of cardinal orthogonal scaling function, and give some useful...
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