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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...
In this paper, under a mild condition,the construction of compactly supported ((1 0 1)/ (-1 -1 1)/ (0 -1 0)) -wavelets is obtained. Wavelets inherits the symmetry of the corresponding scaling function and satisfies the vanishing moment condition originating in the symbols of the scaling function.One example is also given to demonstrate the general theory.
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