I am using wavelets to analyse some complicated 1D signal, where I am able to come up with multiple filtered signals with different level of details. However, the cutoff of wavelet filters follow a octave distribution, doubling in every additional level. I would like to have a continuously tunable similar filter such that by tuning a parameter, the filtered signal smoothly transit from the coarsest to the finest signal interpolating those from the wavelet filters. Is this possible and efficient to implement?

  • $\begingroup$ Are you using a discrete wavelet transform? $\endgroup$ – Laurent Duval May 10 at 7:19
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    $\begingroup$ Yes. I am using R's "dwt" and "idwt" with thresholded wavelet coefficients as a filter. $\endgroup$ – user138668 May 10 at 20:10
  • $\begingroup$ Then you have several options, from continuous wavelet transforms (CWT) with discrete approximation, to a lot of better sampled, often redundant discrete wavelets. Do not focus only on the nature of wavelets, the choice of the type of thresholding plays a great part as well $\endgroup$ – Laurent Duval May 10 at 20:15
  • $\begingroup$ One option (though I can't recommend R packages) rdocumentation.org/packages/Rwave/versions/2.4-8/topics/cwt $\endgroup$ – Laurent Duval May 10 at 20:16
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    $\begingroup$ Whatever, Matlab-like code can work in Octave. From what I understand, you somewhat want to do some matched filtering in the wavelet domain. We tried that here arxiv.org/pdf/1108.4674.pdf or here hal.archives-ouvertes.fr/hal-00914628 Would that match? $\endgroup$ – Laurent Duval May 10 at 20:52

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