Symmetric Interpolating Scaling Functions
نویسندگان
چکیده
In many applications, wavelets are usually expected to have the following properties: compact support, orthogonality, linear-phase, regularity, and interpolation. To construct such wavelets, it is crucial designing scaling functions with the above properties. In twoand three-band cases, except for the Haar functions, there exists no scaling function with the above five properties. In -band case ( 4), more free degrees available in design enable us to construct such scaling functions. In this paper, a novel approach to designing such scaling functions is proposed. First, we extend the two-band Dubuc filters to -band case. Next, the -band FIR regular symmetric interpolating scaling filters are parameterized, and then, -band FIR regular orthogonal symmetric interpolating scaling filters (OSISFs) are designed via optimal selection of parameters. Finally, two family of four-band and five-band OSISFs and scaling functions are developed, and their smoothnesses are estimated.
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