Tell me this is not true: r2016b and CWT (continuos wavelet transform)
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I was checking out the mathworks site for the new version of the CWT function http://www.mathworks.com/help/wavelet/ref/cwt.html and realised that cwt no longer supports user selectable wavelets such as cmorx.x, dbx, dmey etc. You only have three options : morse', 'amor', and 'bump'
Moreover you no longer can obtain the CWT of a signal at a specified scale, or, for that matter, at user selectable scales likewise c=cwt(signal,'scales,wavelet_type)
Strangely enough in the r2016b WaveletAnalyzer(ex wavemenu) the wavelet selection includes all the previous wavelets (cmorx.x, dbx, dmey, gaussx, haar). Moreover the user can select the scale, likewise in the old cwt.
Does that mean that there is no command line cwt command that apply these wavelets, and user scale selection???
Walter Roberson on 11 Oct 2016
The R2016b release notes say
Continuous Wavelet Transform: Analyze signals with improved automatic selection of wavelet and scales
This release provides an updated version of the continuous wavelet transform, cwt, and a new inverse transform, icwt, for reconstructing the original signal. These functions are easier to use because they have simple interfaces and include default values for the wavelet and scales and frequency and period ranges are easy to specify. When you use the updated cwt, which use analytic wavelets and L1 normalization, icwt produce a more accurate reconstruction.
The old version of cwt continues to work, however, updating existing code to use the new version of cwt is recommended. Both the old and updated versions use the same function name. The inputs to the function determine automatically which version is used.
The documentation page for cwt says you can also look at https://www.mathworks.com/help/wavelet/ref/cwtold.html
Edited: Wayne King on 13 Oct 2016
Paramonte, I posted this response on another thread where you posted a comment. I will repeat the essential content here. As I said in the other post, I would be very interested in engaging with you so please do contact me.
There was already CWTFT in the toolbox for a number of releases that used an FFT-based algorithm (that DFT-based approach to the CWT long preceded Torrence and Compo by the way). The new CWT algorithm features Morse wavelets, which have parameters that can be adjusted to give a very large family of analytic wavelets. In fact, most analytic wavelets in use are just special cases of Morse wavelets as was proved by Lilly and Olhede. We have received a lot of feedback from customers that they are confused by having to specify scales and in fact they quite often get the scale concept wrong and use scales that don't allow them to actually find the phenomena they are looking for. The old CWT had absolutely no defaults. The user had the burden of specifying everything. As I mentioned for many non-experts, having to pick a wavelet was daunting, never mind having to construct a meaningful scale vector. Scale for the wavelet transform should be logarithmically spaced for example and the scales should take into account the support of the wavelet. Neither of those things were built into the old CWT.
For time-frequency (time-scale) analysis which is a major use case for continuous wavelet analysis, many of the orthogonal or biorthogonal wavelets which are quite useful for discrete analysis are inappropriate and lead in many instances to people obtaining a misleading analysis of their data. Orthogonal and biorthogonal wavelets are designed for dyadic scales, which are much more widely spaced that the typical scales in continuous wavelet analysis.
Having said all that, if you want to use the old CWT, that interface still works. In fact, the new CWT parses the input and determines if you are using the old syntax. If so, it will give you the older algorithm. I would sincerely welcome the opportunity to discuss these things further. Feel free to contact me through my profile. I will respond. I would very much be interested in any specific use cases where the old CWT allows one to obtain some insight not obtainable with the new CWT. I am always very interested in getting feedback from users on how to make things better.
We never "not recommend" something lightly. That is not to say that somehow we are infallible, but a lot of thought and customer feedback goes into those decisions.
Hope that helps, Wayne
Dear Paramonte, with respect to naming this is always a hard decision. The acronym CWT is well established so users look for it. Users also expressed some confusion at why we had CWT and CWTFT, and which one should they use. The new CWT algorithm also lends itself to an inverse algorithm which the old one did not, so now we have CWT and ICWT for the inverse. The ICWT accepts a frequency or period band input so you can do a frequency-localized reconstruction.
As I suggested, we specifically implemented the new CWT in a way that you can simply call the old one if you wish.
I would welcome a detailed discussion with you as I offered. But we have seen many users struggle with scale and specifying scales. For example, users will specify scales without taking into account the support of the analyzing wavelet. As a result they would have many scales where the wavelet extended well beyond the extent of their data. So in fact, they had no wavelet at all (there was not even one oscillation in the extent of the data). Or they would similarly use scales which were too small and therefore did not provide any wavelet analysis.
Also, as you are no doubt aware, the scale-to-frequency conversion is not equally good for all wavelets. For the Morse wavelets and the default we use, it is quite good because that wavelet is symmetric and well-localized in the Fourier domain. That is also true of the 'bump' wavelet and 'amor' (Morlet) wavelets supported by the new CWT.
For example, here is the default Morse wavelet in the Fourier domain with a vertical line at its predicted center frequency
omega = 0:0.001:(2*pi);
psihat = omega.^20.*0.0051.*exp(-omega.^3);
plot(omega,psihat); grid on; hold on;
title('Default Morse Wavelet -- Fourier Domain');
plot([(20/3)^(1/3) (20/3)^(1/3)],[0 2.5],'k')
You see that this is perfectly symmetric in the Fourier domain. That is certainly not the case with most of the orthogonal and biorthogonal wavelets, like the 'db' family. In those cases, scale to frequency is not so well defined because the wavelet is not symmetric in the Fourier domain and the bandwidth is much larger.
Also, in the new CWT we use L1 normalization which is much more natural in time-frequency analysis than the L2 normalization used in the older CWT. With L1 normalization, a sine wave of amplitude A, results in wavelet coefficients at the appropriate scale with magnitude A. In the older CWT, the magnitude of an oscillatory component in the wavelet coefficients depended on the scale.
We believe there are many other advantages of the new implementation in addition to the few I have mentioned. I would be very happy to discuss those and compare and contrast those at length with you.
Thank you again for your interest and for engaging in this way. As you said it is helpful for all.