# Tagged Questions

For questions related to wavelets and wavelet theory

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### Strange values of approximating coefficients returned by matlab's wavelets decomposition

I'm trying to get wavelet decomposition of arcsin(x) using, say, haar wavelets When using both Matlab's dwt or wavedec functions, I get strange values for approximating coefficients. Since applying ...
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### An exercise. A property of the Fourier transform of wavelet

In the book "An Introduction To Wavelet Analysis" by David F. Walnut, there is, Exercise 7.45. Show that if $\psi(x)$ is a wavelet, then $\sum\limits_{j}{\left|\hat{\psi}(2^j\gamma)\right|^2} = 1$ ...
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### Finding correlations between many unknown functions.

Given an arbitrarily large number of black-box functions of one variable, is it possible to produce expressions that approximate their relationships to each other over their shared domain? Is it ...
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### $L_2$-norm representation of the function

Let $$f^{\alpha}_+(x)=\frac{1}{\Gamma(\alpha+1)}\sum_{k\ge 0}(-1)^k{\alpha+1 \choose k}(x-k)^{\alpha}_+,$$ where $\alpha > -\frac 12$(see for reference http://bigwww.epfl.ch/publications/...
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### DFT and DWT difference?

what is the basic difference between the Discrete Fourier Transform and the Wavelet Transform ? and why does JPEG2000 preferred DWT over DCT or DFT ?
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### What is a “vanishing moment”?

In this paper, Sweldens says about desireable properties of wavelets: To analyze and represent such signals we need wavelets that are local in space and frequency. Typically this is achieved by ...
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### How do I divide Laurent polynomials?

I have an example from a paper (listed below) that I cannot figure out. I can divide normal polynomials, but the alternative ways to divide Laurent polynomials is beyond me at the moment. The paper ...
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### Extrapolating signals using wavelets

I am an absolute beginner to wavelets, and I've read a few articles on how wavelets are used for predicting future points of a dataset, notably Wavelet prediction for Oil Prices and 1D Signal ...
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### Why is the dot product of 2 wavelet domain functions a real value?

I'm working on some code here, and here is what I have done. It is based on the work by Ng et al. An example of what this looks like is here. Background: Here, a "lighting cubemap" is a bunch of ...
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### What other wavelets (besides the Haar system) form a basis of $L^2(0,1)$?

The Haar system of wavelets forms a basis of $L^2[0,1]$. What other wavelets are there that also form bases of $L^2[0,1]$ (or $L^2[0,a]$ in general)?. Thanks
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### Is there a wavelet frame for $L^2[0,\infty)$?

What systems of wavelets provide a frame for $L^2[0,\infty)$. For example, the Haar system of wavelets provides a basis for $L^2[0,1]$, and the harmonic wavelets provide a basis for all of $L^2(R)$....
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### Best way to find magnitude and phase of a specific frequency in an empirical time series…

I've a discrete, univariate time series, and I'm interested in to investigate a specific frequency component. Assume I'm interested in a frequency with a cycle-time of $f$ samples - and I need to get ...
I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...