Symmetrization and enhancement of the continuous Morlet transform for spectral density estimation (Q2893487)

The continuous wavelet transform involving Morlet basis and corresponding inverse transform have been symmetrised by using an appropriate normalizing factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet amplitude which keeps its power constant for a given scale. A renormalization has been introduced which compensates for the reduction in response outside the cone-of-influence. The renormalized power spectral density has been shown to be enhanced by deconvolution with the wavelet response matrix, which yields the maximum spectral resolution of the harmonic content. The utility of renormalization has been explained by means of examples. It has been shown that the mean wavelet power agrees with the discrete Fourier transform on the distribution of power for a signal, and the integrated instant power agrees with the RMS power of the signal components.