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设φ（ｘ）是尺度函数，它满足双尺度差分方程φ（ｘ）＝∑ｋ∈Ｚｈｋφ（２ｘ－ｋ）（Ｚ是整数集）（）（）式的Ｆｏｕｒｉｅｒ变换为＾φ（ω）＝Ｈ（ω／２）＾φ（ω／２），其中＾φ（ω）是函数φ（ｘ）的Ｆｏｕｒｉｅｒ变换，而Ｈ（ω）＝１／２∑ｋ∈Ｚｈｋｅ－ｉｋω叫做小波的共轭滤波器（简称滤波器）。一般可以从滤波器入手来获取它的展开系数序列｛ｈｋ｝，并由此来构造出各种小波。美国数学家Ｄａｕｂｅｃｈｉｅｓ针对Ｈ（ω）为ｅ－ｉω的多项式形式的滤波器（称为多项式滤波器），给出了产生紧支小波的方法以及相应正则阶的估计。采用有理分式形式的滤波器来构造小波。这种分式滤波器具有如下优点：１．不仅可以构造出包括Ｄａｕｂｅｃｈｉｅｓ小波在内的小波函数，而且能包括Ｂ样条小波；２．可构造出具对称性的小波函数；３．通过恰当的构造，小波函数正则阶比Ｄａｕｂｅｃｈｉｅｓ小波有显著的提高。
Let φ (x) be a scaling function that satisfies the Fourier transform of the two-scale difference equation φ (x) = Σk∈Zhkφ (2x-k) (Z is an integer set) ) = H (ω / 2) ^ φ (ω / 2), where φ φ (ω) is the Fourier transform of the function φ (x), and H ω = ½Σk ∈Zhke-ikω is called wavelet Conjugate filter (referred to as filter). It is generally possible to start with the filter to obtain its expansion coefficient sequence {hk}, and to construct a variety of wavelet. American mathematician Daubechies gives a polynomial filter (called a polynomial filter) with H (ω) as e-iω, and gives the method of generating clamped wavelet and the estimation of the corresponding regular order. Wavelets are constructed using rational fractional filters. This fractional filter has the following advantages: Not only can construct the wavelet function including Daubechies wavelet, but also include the B-spline wavelet; Can construct a symmetrical wavelet function; 3. With proper construction, the order of wavelet function is significantly higher than that of Daubechies wavelet.