Abstract
In order to organically combine the minimum‐energy frame with the significant properties of multiwavelets, minimum‐energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum‐energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum‐energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum‐energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B‐spline functions.
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