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With a signal x of length $2^{16}$, the DWT (computed for example with pyWavelet's wavedec) has only 16 or 17 rows (the wavelet scale is dyadic). Is there a DWT with more scales? (ex : 1024 rows instead of 16!)

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  • $\begingroup$ Why do you need a more precise scale? $\endgroup$ – Peter K. Nov 23 '13 at 22:00
  • $\begingroup$ Because I want to use the scale axis of the wavelet transform (y-axis in a scalogram) as a frequency axis : with few scales (see mathworks.fr/help/releases/R2013b/wavelet/ref/cwt.gif) I get poor frequency resolution $\endgroup$ – Basj Nov 23 '13 at 22:05
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You will need to use a continues wavelet transform (cwt) where you can specify the resolution of the scales (as done in the image you posted mathworks.fr/help/releases/R2013b/wavelet/ref/cwt.gif). The DWT only has $J$ scales by definition for $2^J$ signals.

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  • $\begingroup$ Thanks a lot! This is a confirmation of what I thought : I really need CWT. $\endgroup$ – Basj Nov 24 '13 at 12:17
  • $\begingroup$ The problem I have now with my $2^{16}$ length signal is : 1/ With DWT => too few scales (only 16!) 2/ With CWT, I can get as many scales that I want, BUT there will be too many time frames ! Example : I I do the CWT with 1024 scales ($s=s_0 2^{j/v}$) , the output array will be of shape $(1024, 2^{16})$ $\endgroup$ – Basj Nov 24 '13 at 13:12
  • $\begingroup$ You could subsample the output, taking maybe every 32 columns. $\endgroup$ – Gummi F Nov 24 '13 at 20:28
  • $\begingroup$ Yes Gummi F, if I subsample (taking every 32 columns) I will have $(1024, 2048)$ instead of $(1024,2^{16})$, this is cool, but then will I be able to reconstruct the original signal with this subsampling ? (probably yes, because even with this subsampling, I still have more $1024 * 2048$ coefficients, ie more than the original signal, and probably redudancy...) but how to reconstruct the original signal ? $\endgroup$ – Basj Nov 24 '13 at 21:01
  • $\begingroup$ I'm not sure, usually cwt is only used for analysis because it is redundant. $\endgroup$ – Gummi F Nov 25 '13 at 2:14

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