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In my studies of wavelets, there appear to be 3 different families of them:

  1. The Continuous wavelet transform
  2. The Discrete wavelet transform
  3. The Redundant wavelet transform

They are all based on the same concept, but vary in how they are shifted/scaled, and/or decimated or not at every scale level.

My question is, where does each type find utility? For example, why would I want to use the Redundant Wavelet Transform over the Discrete Wavelet Transform, over the Continuous wavelet Transform in a particular application?

What advantages/disadvantages does one type of transform have over another, as far as its applicability is concerned?

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We had this discussion not long ago. I don't have time to answer in full at the moment, but take a look at the discussion here: dsp.stackexchange.com/questions/7626/… –  user2718 Jan 28 '13 at 20:17
    
@BruceZenone In that question I was asking about terminology, here I am inquiring as to specific applicability of the above transforms. Example: Let us say we wanted to compress a signal. Why use the CWT over the DWT over the RWT? etc. This is a question about applicability of the transforms in specific applications. –  Mohammad Jan 28 '13 at 20:45
    
Got it. I'll let someone else chime in. I'd like to see more perspective on this question as well. –  user2718 Jan 29 '13 at 0:01
    
You may like to read the book "The World According to Wavelets" by Barbara Hubbard for a more historical and application oriented treatment of the subject. –  user2718 Jan 29 '13 at 13:09
    
@BruceZenone That looks like a very interesting book, Ill make sure to procure it! :-) –  Mohammad Jan 29 '13 at 13:44

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