The Wikipedia article on Wavelet Transform states that: Wavelet compression is not good for all kinds of data: transient signal characteristics mean good wavelet compression, w …

Why is it important for the scaling function to have unit area in wavelets?

Using the mother wavlet $phi$ one obtains an orthonormal basis $\phi_{j,k}(x):=2^{j/2}\,\phi(2^j\,x-k)$of L^2 (on the unit interval say). Given a function $f$ on can calculate the …

Are there any suggestions for introductory books on wavelets? I want a book, not online material or tutorials.

What systems of wavelets provide a discrete frame for $L^2[0,\infty)$? Specifically, I need a mother wavelet $\psi(x)$ that has a continuous second derivative, such that the syst …

The Dunkl intertwinig operator $V_k$ on $C(\mathbb{R}^d)$ is defined by: $$V_k f(x)=\int_{\mathbb{R}^d}f(y)d\mu_x(y),$$ where $d\mu_x$ is a probability measure on $\mathbb{R}^d$ …

Hello mathoverflow community ! I have a simple question that seems to have a non trivial answer. Given a discrete one dimensional signal $w(x)$ defined in a finite range, and the …

A travelling wave is given by; $ C(x,t) = \exp(i(k_0x-w_0t)) \ \int_{-∞}^∞ A_0 \exp(-a(k-k_0)^2)\exp(iE(k-k_0)) \ \mathrm{d} k$ I need to get it into the form; $ C(x,t) = A_0 \s …

Hi! I want to do a time-frequency analysis of an EEG signal. I found the GSL wavelet function for computing wavelet coefficients. How can I extract actual frequency bands (e.g. 8 - …

This question is about conditions on a mother wavelet that generates a countable familily of child wavelets via scaling and translation, that are both necessary and sufficient for …

For every positive integer A there exists a unique polynomial Q_A(X) of degree A-1 satisfying the identity (1-x/2)^A Q_A(x) + (x/2)^A Q_A(2-x) - 1 = 0 How to prove this ? A simp …

Hi! I was instructed via reddit that this place would be the best place to post this question. Fingers cross you can help... Ive been writing some code to get rid of noise "spikes …

I want to simulate a 2d linear wave equation on a circle ($\displaystyle\frac{\partial^2 z(x,y,t)}{\partial t^2}=v^2\cdot\left(\displaystyle\frac{\partial^2 z(x,y,t)}{\partial x^2} …

I'm using a wavelet transform in Matlab, so I think of it as a black-box. I'll represent it here as $W(x)$. There's a reconstruction function as well, which I'll write as $W^\da …

It's a long time since I worked on this kind of problem, so please bear with me. I have an approximate inverse matrix that I'm using as a preconditioner to solve the conjugate gra …