# Questions tagged [dwt]

DWT denotes discrete wavelet transforms, instances of continuous wavelet transforms that admit a discrete sampling.

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### At what stage do we compute the approximations and details while performing a DWT?

$$\int_{-\infty}^{+\infty}{f(t)\psi_{j,k}^\ast(t)dt}\ \textrm{with}\ \psi_{j,k}(t)\ =\ a_0^{-j/2}\psi(a_0^{-j}t\ -\ b_0k)$$ If this is the expression for the wavelet transform, how does this lead to ...
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### Aliasing from downsampling and Nyquist

In a book Conceptual Wavelets in Digital Signal Processing by Lee Fugal 2009 on page 246 the author talks about aliasing present in DWT subbands due to downsampling by 2 and states: Recall from DSP ...
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### Discrete Wavelet Transform: Specifics of Filter Bank

So I have been given to understand that the discrete wavelet transform is able to provide both time and frequency resolution in ways that classic Fourier and even short time Fourier cannot. By ...
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### What are the best suitable type of image moments (Hu, Zernike etc.) that can be applied on an Image after DCT/DWT?

I want to perform a block by block comparison by using overlapping blocks and their respective image moments. Can anybody suggest for type of image moment suited for blocks of DCT/DWT of that image. ...
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### why double desity DWT use two HPF?

The double-density DWT is an improvement upon the critically sampled DWT with important additional properties: It employs one scaling function and two distinct wavelets, which are designed to be ...
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### 2D DWT computation order

In 2D the discrete wavelet transform (DWT) of an image using lifting based 5/3 filter, if I perform a row-wise operation first then perform column-wise operation then I will get 4 sub-band LL, LH and ...
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### DWT initialization from nonuniform samples

Let $D\subset\mathbb R$ be compact, let $f:\mathbb R\to\mathbb R$ be a contintinuous function with support $D$. Let $\phi(x)$ be a well-defined scaling function, in the sense that it generates a ...
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### Wavelet synthesis boundary conditions

I am interested in discrete wavelet decomposition using the D4 wavelet and am having issues understanding how the boundaries are handled during the synthesis step. Say I want to use a smooth boundary ...
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### Obtaining Continuous Wavelet Transform coefficients from Discrete Wavelet Transform

On an earlier StackExchange question, I read that for a given signal, "From the resulting DWT the corresponding full CWT can be obtained by convolving the DWT with the reproducing kernel of the ...
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### Discrete Wavelet Transform (DWT) Filter Bank

I have some stumbling block in my thesis writing. Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to ...
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### What are the constraints in design of discrete orthogonal wavelets?

Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank? So not all wavelets can be implemeted perfectly (invertible) with ...
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### Wavelet transform of a spatial convolution

Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? In other words can I find a simple form of \$W\left[ \int f(t) g(x-t) \, ...