Abstract: Based on lifting scheme, the new prediction operator and update operator are constructed to modify the second generation wavelet algorithm by spline interpolation. The new second generation wavelet not only has the characteristics of the amplitude attenuation, local non-zero and volatility, but also has high regularity. Simultaneously, the new second generation wavelet transform is developed by spline interpolation, and it’s effectiveness for extraction of high-frequency signal is verified. Specific method for function approximation by sparse expression of the new second generation wavelet is given. Numerical experiments show the feasibility and effectiveness of the algorithm.
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Key words: the second generation wavelet transform, lifting scheme, spline interpolation, function approximation