My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing applies, but for dilated version of the wavelet. I thought that scalograms can be defined for all types of wavelet transforms, that is, for the:
- Continuous wavelet transform
- Discrete wavelet transform
- Redundant wavelet transform
However upon further investigation is seems that the scalogram is only definable for the CWT. Based on this I have multiple inter-related questions that google has not sufficed for ATM.
- Is it true that the scalogram is not defined for the DWT or RWT? If so, why not?
- Let us say an $N$ length signal has a 10-level decomposition by using DWT. If all levels are plotted as an image, (that is, a $10xN$ image), what is this image called?
As an example of a DWT 'scalogram', here is one for AWGN:
- Concerning the same signal, suppose we instead plot the approximation MRA of the signal at all levels. (So again, a $10xN$) image. What is this image called in proper terminology? For example, here I have shown approximation MRAs and detail MRAs for AWGN. (Clearly they are not the same as 'scalogram' of DWT).