Design of Halfband Filters for Orthogonal Wavelets via Sum of Squares Decomposition

This letter is concerned with design of halfband product filters for orthogonal wavelets. We first remark that the recent zero-pinning technique for orthogonal wavelet design cannot always guarantee the nonnegativity of the filter. We then propose to use sum of squares (SOS) decomposition to ensure its nonnegativity. The use of SOS decomposition also allows us to solve two optimization problems on the halfband filter via semidefinite programming. For a given length with pre-specified number of zeros at , we obtain halfband filters with maximal passband width. Design examples are provided.