Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition. (English) Zbl 1410.42033
Summary: In [“On alternative wavelet reconstruction formula: a case study of approximate wavelets”, R. Soc. Open Sci. 1, No. 2, Article ID 140124, 5 p. (2014; doi:10.1098/rsos.140124)], the second and first authors proved that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows an existence of the exact inverse transform. Here, we consider the computational possibility for the realization of this approach. We provide a modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications include the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 65T60 | Numerical methods for wavelets |
Software:
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