Second-generation wavelet transform

Actually, the sequence of lifting steps could be converted to a regular discrete wavelet transform, but this is unnecessary because both design and application is made via the lifting scheme.

This means that they are not designed in the frequency domain, as they are usually in the classical (so to speak first generation) transforms such as the DWT and CWT).

The idea of moving away from the Fourier domain was introduced independently by David Donoho and Harten in the early 1990s.

For certain wavelets the lifting steps (interpolating and updating) are repeated several times before the result is produced.

The idea can be expanded (as used in the DWT) to create a filter bank with a number of levels.

The SGWT has a number of advantages over the classical wavelet transform in that it is quicker to compute (by a factor of 2) and it can be used to generate a multiresolution analysis that does not fit a uniform grid.

Using a priori information the grid can be designed to allow the best analysis of the signal to be made.