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I understand that aliasing occurs in DWPT if the wavelet used is of low order since the "filters" are not perfect and the combination of down sampling and overlapping between bands causes aliasing. I am using low order wavelet as I aim to implement the process in real-time and I have limitations on the number of filter taps. Doing some simulations in matlab I saw aliasing in two cases:

  1. One case I saw it when I decomposed a signal to a tree and I plotted FFT of a certain node but when I reconstructed the tree I noticed that aliasing was canceled.(basically did not alter the coefficients only decomposed viewed and reconstructed). enter image description here enter image description here
  2. Doing the same thing as above but thresholding the node or compressing the coefficients to zero the aliasing was still present after reconstruction. enter image description here enter image description here I compressed level 22 coefficients to zero. enter image description here So can I conclude that aliasing will always occur if I am using a low order wavelet say 'db4' and I manipulate the coefficients? If so how is wavelet such famous denoising tool and aliasing can be this bad?
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    $\begingroup$ Would it be possible to post some plots and/or spectra from those cases where you observed that aliasing? Also, when you say that the db4 is a "low order wavelet", what exactly do you mean? Low order in what sense? Or maybe in what conditions? $\endgroup$ – A_A Jul 27 at 9:46
  • $\begingroup$ By low order I meant to say low number of vanishing moments, in the sense that the scaling and wavelet decomposition filters are "less ideal" and would allow more aliasing (since more overlapping between them happens) than when the vanishing moments are higher. I will add picture to the post shortly. Thank you $\endgroup$ – Shannon Jul 27 at 21:19
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    $\begingroup$ Thank you for taking the time to edit your question. I am still not clear what you mean by "aliasing" however. If aliasing is allowed to creep into a DSP chain, it makes it impossible to know if a sinusoidal component is genuine or if it has "folded" and it appears at a lower frequency. I cannot see evidence of this here (?). Can I please ask how do you run the FFT on the DWT components? $\endgroup$ – A_A Jul 28 at 11:16
  • $\begingroup$ In the first case, I decomposed the input signal into branches and reconstructed it without any alteration and the FFT is of the reconstructed input signal so I saw that it was at 50Hz only (as it should be). The second case, I zeroed out branch 22 where the 50Hz would fall and reconstructed the signal. The FFT seemed to have other signals that was decomposed into other branches. I do see now why I am not making sense. I am putting a 50 HZ and canceling it and expecting an output that would make sense. $\endgroup$ – Shannon Jul 28 at 19:52
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    $\begingroup$ I see. Would a better way of putting it be "Why should wavelet re-synthesis produce an output when the main component is suppressed and what does this mean for denoising" (?). I think that focusing on an "aliasing" aspect might detract from a more useful answer here. If this sounds like a better fit, do you mind editing the question to better reflect what you are trying to discover? $\endgroup$ – A_A Jul 29 at 16:34

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