SYMMETRIZATION AND ENHANCEMENT OF THE CONTINUOUS MORLET TRANSFORM FOR SPECTRAL DENSITY ESTIMATION

摘要

The forward and inverse wavelet transform using the continuous Morlet basis may bensymmetrized by using an appropriate normalization factor. The loss of response duento wavelet truncation is addressed through a renormalization of the wavelet based onnpower. The spectral density has physical units which may be related to the squarednamplitude of the signal, as do its margins the mean wavelet power and the integratedninstant power, giving a quantitative estimate of the power density with temporal resolution.nDeconvolution with the wavelet response matrix reduces the spectral leakage andnproduces an enhanced wavelet spectrum providing maximum resolution of the harmonicncontent of a signal. Applications to data analysis are discussed