Pagina web del Prof. Invitado

φ(x)=2∑k=0Wavelet: : definiciones y relacionesConsider two functions which are solutions to the following equations:L−1L−1∞φ(x)is normalized: φ ( x ) dx = 1hφ(2x−k),kψ(x)=j−j2 j − jLet φ ( x)= 2 φ ( 2 x − k )kk2∑k=0gφ(2x−k)kj−j2 j − jand ψk( x)= 2 ψk( 2 x − k)where j, k are integers denoting the dilations and translations.L −The coefficients { } 1 L −H = h kand G = { g } 1 k = 0k k = 0are the filters and are related by:kgk= ( −1)hL−k, k = 0,1,..., L −1and are chosen so that,∞jj mψkwill satisfy ∫ ψ k( x)ψl( x)dx = δklδjm0Also ( x)ψ 0( x)∞∫−∞−∞ψ = satisfiesmψ ( x)x dx = 0, m = 0,1,..., M − 1The spaces spanned by φ and ψ over k with fixed j are:Vj= spank∈Zjφ ( x),kWj= spank∈Zjψ ( x)k−∫∞(Orthonormal. Basis)(M vanishing moments.)