Continuous wavelet transform Guide, Meaning , Facts, Information and Description
In
mathematics, the
continuous wavelet transform (CWT) is a
wavelet transform defined by
-
where represents translation, represents scale and is the
mother wavelet.
The original function can be reconstructed with the inverse transform
-
where
-
is called the admissibility constant and is the fourier-transform of .
For a successful inverse transform, the admissibility constant has to satisfy the admissibility condition:
- .
Note also that the admissibility condition implies that , so that a wavelet must integrate to zero. For reference, the relationship between the so-called
mother wavelet and the
daughter wavelets is as follows:
- .
This is an Article on Continuous wavelet transform. Page Contains Information, Facts Details or Explanation Guide About Continuous wavelet transform
