Performance of reconstruction factors for a class of new complex continuous wavelets

Abstract

In this paper, we determine the factors necessary for the reconstruction of the signal from its continuous wavelet transform performed using the new complex continuous wavelet family by making use of admissible conditions and studied some of its properties. We also make a comparative assessment of its performance with the existing complex continuous wavelets, such as Morlet, Paul and DOG, in terms of reconstruction capability. The reconstruction was performed on three data sets, namely, a signal with a mixture of low and high frequencies, a non-stationary signal (synthetic) and an ECG signal. The results show that the proposed family of wavelets reconstruction capability is comparable with Morlet, Paul and DOG wavelets. Further, we investigate an alternate reconstruction formula without making use of admissibility condition and compare its efficiency of reconstruction with the standard (restricted) Morlet wavelet.