Wavelet Generations




First Generations

These wavelets can be used for periodic or infinite signals but they cannot be optimized in bounded domains

This wavelet transform is used in self-similarity detection, image compressions, signal de-noising, identification of pure frequencies and detection of discontinuities. Other applications are: Acoustic signal compressions, in fingerprint image compression, image processing, enhancement and restoration. Fractal analysis and de-noising noisy data.


Second Generations

Fastest for moderately short-filters but one needs to first find the factorizations of the filter banks matrices, but these factors are very well documented for JPEG2000 wavelets.

They are used tremendously for efficient coding in compressions algorithms, computer graphics, geographical data analysis and lossy data compressions. The FBI has used the CDF wavelets in fingerprint compression scans. With these wavelets, compressions ratios of about 20 to 1 could be achieved. They have been applied in multi-resolution analysis, system identifications, and parameter estimations.


Third Generations

They do not oscillate and do not show aliasing and degrees of shift variance in their magnitudes. They exhibit a 2D attribute of the signal to be transformed and produce redundancies

They are applied in sparse-representation, multi-resolution and useful features characterizations based on the image structures. They are also used in medical profession because they provide intuitive bridges between time and frequency data that could clarify interpretations of complex head-trauma spectra produced with Fourier transform. They are also used in music industry for transcriptions of music since they produced precise results that were not possible earlier with the Fourier transforms. It is capable of capturing short-bursts of repeating and alternating music notes.


Next Generations

They will be too specific and too constrained because These wavelet transforms are still very much at the research stage and meant for specific applications

The applications will include human-vision characterizations, frequency localizations, feature extractions, analysis of seismic information, analysis of biomedical information, wireless sensor networks [17] [18] [20] [21] [22] [23] etcetera.