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### What mathematical background is preliminary for reading and understanding books/papers on wavelets? [migrated]

Please excuse my english. I have had the following math courses for mechatronics engineering education: Calculus (single and multivariable) Linear algebra (introductory) Differential equations (ode'...
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### Computing 3-term Connection Coefficients for Wavelets

I am trying to calculate the three-term connection coefficients $$Λ_{l,m}^{d_1,d_2,d_3} = ∫_{-∞}^∞ φ^{(d_1)}(x) φ^{(d_2)}_l(x) φ^{(d_3)}_m(x) dx$$ for Daubechies wavelets numerically using Python. ...
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### In which sense Daubechies wavelets converge to the Shannon wavelet?

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 ...
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### Why is it important to know if a frame is a Parseval frame?

I understand that a Parseval frame is one in which both upper and lower frame bounds equal 1. What's the main advantage to having this be the case? Or, more specifically, if I'm constructing a frame ...
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### Wavelets in the spaces of harmonic functions

I plan to do something with the theory of wavelets but in harmonic function theory. My question is about this interconnection between wavelets and harmonic functions. Can you recommend me some paper ...
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### phase prediction of wavelet coefficients for 1D signal [closed]

I was reading a paper 'A Flexible Framework for Local Phase Coherence Computation' (article URL) on predicting phases of wavelet coefficients across 3 consecutive scales in the 1D case, and I'm trying ...
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### How to bound Haar coefficients in terms of total variation?

I'm trying to get the basic idea behind the proof of Theorem 8.1 of this paper, but I'm having difficulty. Specifically, it says: We shall show that there is a set $\Lambda_n\subset\mathcal{D}$ ...
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### Approximation power of wavelets

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, while smooth, ...
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### Scaling function

Why is it important for the scaling function to have unit area in wavelets?
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### Discrete Wavelet Transform and L2 Basis

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 coefficients using ...
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### The Dunkl intertwining operator $V_k$ on $C(\mathbb{R}^d)$

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 $\mathbb{R}^d$ with support in the ...
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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 system of wavelets $\{\... 3answers 694 views ### Decomposing a discrete signal into a sum of rectangle functions Hello mathoverflow community ! I have a simple question that seems to have a non trivial answer. Given a discrete one dimensional signal$w(x)$defined in a finite range, and the boxcar (rectangular)... 0answers 763 views ### Interpolating Wavelet Coefficients Hi! I was instructed via reddit that this place would be the best place to post this question. Fingers cross you can help... Ive been writing some code to get rid of noise "spikes" in a signal. I'm ... 1answer 346 views ### When does a mother wavelet generate a frame? This question is about conditions on a mother wavelet that generates a countable familily of child wavelets via scaling and translation, that are both necessary and sufficient for the child wavelets ... 1answer 316 views ### [Numerical Mathemtics] How to solve hexagonal central differences I want to simulate a 2d linear wave equation on a circle ($\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}+\displaystyle\frac{\...
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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 $W^\dagger(y)$. I can ...