Mother wavelet definitions used in Advanced Siglan Processing Toolkit

Question

I didn't find the functional form nor the center frequency of the predefined mother wavelets used in AWT and CWT anywhere from NI documentation. I assume that wavelet analysis used in Advanced Signal Processing Toolkit follows the general framework of wavelet analysis. However the wavelet analysis is not well determined if the form and the scale of the mother wavelet are not known. Mother wavelet can be almost anything as long as it follows certain mathematical rules set to wavelets. The scaling of the mother wavelet can be freely selected by the author of the analysis toolkit. The scaling and the form of the mother wavelet together determine the
center frequency of the mother wavelet. If the scaling and the form of the mother wavelet are not known, the components of the wavelet analysis cannot be correlated to corresponding pseudo-frequencies. In the documents I have read the form of the mother wavelets used by the analysis toolkit were not fully described, nor was the center frequencies of the mother wavelets. Where can I find the definitions and center frequencies of the predefined mother wavelets used in the Advanced Signal Processing Toolkit?
Tomi Maila

Answer 1

I join Tomi's request. The "Advanced Signal Processing Toolkit" is documented till degree, when one wants to play around and to get a feeling what CWT and AWT are. When it comes to the research and product developing purposes the vital information is missing, although the main statements are being inside, like "The AWT is a wavelet transform that provides both the magnitude and phase information of signals in the time-scale or time-frequency domain"(p. 3-6) or "With amplitude normalization, you can obtain the precise magnitude evolution over time for each hyperbolic chirp". Exactly what I need, only the output product does not correspond to the expected value...
Considering AWT, as stated on p. 3-7: "The AWT computes the inner products of the analyzed signal and a set of complex Morlet wavelets..."
In order to get the central frequency of Morlet-transform, I have used Matlab and centfrq('morl') command, which gives fs=0,8125Hz for the Morl mother wavelet. It is available for the other mother-wavelets of coarse. Such an info must be available in LabVIEW Documentation as well. Hope that helps a bit for the first testings.
The wavelet definitions stay unknown for me as well. The same with the meaning and mechanism of the amplitude and energy normalizations in AWT.
greetings
Sergi
using LabVIEW2010