Abstract
In this contribution we introduce the concept of multiresolution analysis (MRA) and give an explanation of the relationship between MRA and orthonormal wavelet basis. The construction of the orthonormal B-spline wavelet bases is described in detail. We extend the B-splines to `non-integral order' cases and thus obtain a new family of orthonormal wavelet bases for the space L2(R). Some good properties of the new wavelets are demonstrated. The new wavelet family gives satisfactory performances in our research projects including seismic signal compression and gravity tide data processing.
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