Second-generation wavelet transform

In <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, the second-generation wavelet transform (SGWT) is a <a href="/facts/Wavelet/3XcX4uIP">wavelet</a> transform where the <a href="/facts/Filter_(signal_processing)/vydJCNle">filters</a> (or even the represented wavelets) are not designed explicitly, but the transform consists of the application of the <a href="/facts/Lifting_scheme/htMkzoAQ">Lifting scheme</a>.
Actually, the sequence of lifting steps could be converted to a regular <a href="/facts/Discrete_wavelet_transform/19DVnk4n">discrete wavelet transform</a>, but this is unnecessary because both design and application is made via the lifting scheme.
This means that they are not designed in the <a href="/facts/Frequency_domain/pyTVrUSq">frequency domain</a>, as they are usually in the classical (so to speak first generation) transforms such as the <a href="/facts/Discrete_wavelet_transform/19DVnk4n">DWT</a> and <a href="/facts/Continuous_wavelet_transform/nGUoUAKX">CWT</a>).
The idea of moving away from the <a href="/facts/Fourier_analysis/sUA8JP6q">Fourier</a> domain was introduced independently by <a href="/facts/David_Donoho/mR4tBykY">David Donoho</a> and <a href="/facts/Harten/oEfaP9K0">Harten</a> in the early 1990s.

Second-generation wavelet transform open-in-new

Second-generation wavelet transform