DWT with more precise scale

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!)

• Why do you need a more precise scale? – Peter K. Nov 23 '13 at 22:00
• 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 – Basj Nov 23 '13 at 22:05

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.
• 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 $(1024, 2^{16})$ – Basj Nov 24 '13 at 13:12
• 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 ? – Basj Nov 24 '13 at 21:01