Symmetrization and enhancement of the continuous Morlet transform

Details Symmetrization and enhancement of the continuous Morlet transform Symmetrization and enhancement of the continuous Morlet transform

2009-12-06

arxiv.org/abs/0912.1126v2

International Journal of Wavelets, Multiresolution and Information Processing (IJWMIP), Volume: 10, Issue: 1 (2012) 1250009

Physics

Data Analysis, Statistics and Probability

12 pages, 8 figures, 2 tables, minor revision, final version

Scientific paper

10.1142/S0219691311004511

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet power and the integrated instant power, giving a quantitative estimate of the power density with temporal resolution. Deconvolution with the wavelet response matrix reduces the spectral leakage and produces an enhanced wavelet spectrum providing maximum resolution of the harmonic content of a signal. Applications to data analysis are discussed.

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