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1 矢量小波函数方程Ψ(x)=sum from k=0 to N(C_kΨ(2x-k)) (1)称为尺度方程,它在多尺度分析中起着举足轻重的作用。方程(1)的系数可以是实数亦可以是复数,(1)式的解Ψ(x)称为尺度函数。若式(1)有一个可积解Ψ(x),且是L~2(R)中的一个规范正交基,则从下式Ψ(x)=sum from k=0 to N(-1)~k(C_(N-k)Ψ(2x-k)) (2)
1 vector wavelet function equation Ψ (x) = sum from k = 0 to N (C_kΨ (2x-k)) (1) is called the scale equation, which plays a decisive role in the multi-scale analysis. The coefficients of equation (1) can be either real or complex numbers. (1) The solution Ψ (x) of the equation is called the scaling function. If equation (1) has an integrable Ψ (x) and is a canonical orthonormal in L ~ 2 (R), then from the following equation ψ (x) = sum from k = 0 to N (-1 ) ~ k (C_ (Nk) Ψ (2x-k)) (2)