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I'm trying to estimate the fractal dimension of a function. I created the log(energies) Vs log(scales) plot and I'm computing the Fractal Dimension (D) from the slope using the relation $$ \alpha = -...

I have a question regarding the Continuous Wavelet Transform (CWT) of non finite energy functions, such as $g(t) = a\exp(i\omega_0t)$. We know that the CWT is defined for functions in the Hilbert ...

For a given frame $\{\zeta_i\}_{i=1}^\infty$, any Bessel sequence $\{\eta_i\}_{i=1}^\infty$ satisfying in the following identity for every $\xi\in H$ $$\xi=\sum_{i=1}^\infty \langle \xi, \eta_i\...

I have a question regarding the possibility of constructing a Discrete Wavelet Transform based on a scaling function having Gaussian decay (and no more decay than that). More specifically, I am ...

My question is about wavelets theory. Consider $\psi_n$ the Daubechies wavelet of order $n \geq 1$; that is, the Daubechies wavelet with $n$ vanishing moments. We also define the Shannon wavelet in ...