Orthonormal wavelet bases with rational dilation factors based on MRA

In many applications, wavelets with rational dilation have more expected properties such as orthogonality and interpolation than dilation 2. This paper studied the rational dilation factor p/q orthonormal wavelet bases based on multiresolution analysis, stated that the orthonormal wavelet bases should consist of p-q functions ψ¹,ψ²,...,ψ^p-q in W₀ = V₁ ⊖ V₀ and established a perfect reconstruction condition for the wavelet bases. In the end, we provided two examples with dilation factor 3/2 to explain our theory.