3 ms·
To explain further, HT is unable to compose complex valued functions - it is only a complete system for real valued functions, that is: R -> R. So naturally, it
by goldenkey 4y ago
To explain further, HT is unable to compose complex valued functions - it is only a complete system for real valued functions, that is: R -> R. So naturally, it's simpler, because it's less expressive.
Let me wow you since HT is not even on the map of exotic or alternative wavelet decompositions.
For example, Hermite transform: https://en.wikipedia.org/wiki/Hermite_transform https://en.wikipedia.org/wiki/Hermite_transform
or if looking in the discrete space:
https://en.wikipedia.org/wiki/Hadamard_transform https://en.wikipedia.org/wiki/Hadamard_transform
See: https://en.wikipedia.org/wiki/Orthogonal_functions https://en.wikipedia.org/wiki/Orthogonal_functions
I'm amazed that folks think Fourier series is so special when it's just one of many in a deluge of complete function systems.
- kragen 4y agothe fourier transform is very special indeed because of what its basis functions are the eigenvectors of
- goldenkey 4y agoSo you use one special thing, the Laplacian, to connote the specialty of another? I can go ahead and do the same duality for those other transforms and their respective basis functions. Specialness in mathematics is a fruitless and fealty affair - G.H. Hardy
- kragen 4y agothat's not it