M-band compactly supported orthogonal symmetric interpolating scaling functions

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 two- and three-band cases, except for the Haar functions, there exists no scaling function with the above five properties. In M-band case (M⩾4), more free degrees available in design enable us to construct such scaling functions. A novel approach to designing such scaling functions is proposed. First, we extend the two-band Dubuc (1986) filters to the M-band case. Next, the M-band FIR regular symmetric interpolating scaling filters are parameterized, and then, M-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 smoothness are estimated