4. Wavelet frames
The continuous wavelet transform (3) , and the short-time Fourier transform (2) , are representations that are not "economical", in the sense that, starting from a one-dimensional signal, we arrive at a function of two real variables. These representations are said to be highly redundant. What's more, computer implementation of analysis and synthesis algorithms using these transformations requires signal sampling at some point. This is an argument in favor of working with discrete decompositions...
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Wavelet frames
Multidimensional wavelet bases
References
Software
Numerous software packages now exist, making it easy to implement a wavelet transformation. Most of these products are integrated into larger software packages (MATLAB, Mathematica...) designed for numerical or symbolic calculation. What's more, these programs are generally available on different systems (Unix/Linux, Windows, Macintosh).
Commercial software includes the Wavelet Toolbox, a MATLAB toolbox...
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