Hypercomplex Wavelets
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=Introduction= | =Introduction= | ||
| + | Complex wavelets are superior to real-valued wavelets because they are nearly shift-invariant. Complex wavelets yield amplitude-phase | ||
| + | information in a similar way as the Fourier transform does. In contrast to the Fourier transform, wavelets allow to analyse the | ||
| + | signal locally and thus can be applied to signals with a non-stationary statistic (such as images of a natural scene). In the same | ||
| + | way as a one-dimensional signal requires complex numbers to represent the local structure of the signal, two-dimensional signals | ||
| + | require hypercomplex numbers. | ||
| + | |||
[[Image:working.gif]] Under construction ... | [[Image:working.gif]] Under construction ... | ||
Revision as of 13:34, 26 September 2007
Introduction
Complex wavelets are superior to real-valued wavelets because they are nearly shift-invariant. Complex wavelets yield amplitude-phase information in a similar way as the Fourier transform does. In contrast to the Fourier transform, wavelets allow to analyse the signal locally and thus can be applied to signals with a non-stationary statistic (such as images of a natural scene). In the same way as a one-dimensional signal requires complex numbers to represent the local structure of the signal, two-dimensional signals require hypercomplex numbers.
Under construction ...
