Matrix-Nullspace Wavelet Construction
Subendran Sivalingam · 1994
Abstract. We discuss a method for constructing (pre-)wavelets by finding the nullspace of a matrix whose elements are generated from scale functions and their scale relation. In particular, we show how the size of this matrix may be known in advance and give examples of its construction. We consider the usual setting of a multiresolution analysis [3] in which a basis of scale functions φj,m(x) = φ(σ j x − m) (assumed of compact support: φ(x) = 0 when x � ∈ [0,M]) generates a space V j, dilated scale functions φj+1,m(x)=φ(σ j+1 x − m) generate a space V j+1, and a scale relation