Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition

Recently, it has been proven Lebedeva and Postnikov (2014) 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.