On alternative wavelet reconstruction formula: a case study of   approximate wavelets
  The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard Morlet wavelet, which is an important example of such analyzing functions, is discussed. 
Elena A. Lebedeva, Eugene B. Postnikov
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