|
In mathematics and numerical analysis, a wavelet is a basis function used to construct a wavelet
transform. A wave is a simple sine function similar to a rope held at both ends and modulated up and down. A wavelet is two
or more ropes being modulated up and down but you are only allowed to see these waves collectively as one.
As opposed to the functions sine and cosine
used for Fourier transforms, a wavelet not only has locality
(small support) in the frequency domain but also in the time or spatial domain. Therefore, wavelets look like fading in and
fading out waves (hence the name).
The simplest wavelet is the Haar wavelet. A wavelet commonly used in the
natural sciences is the Morlet wavelet. There is also the Daubechies wavelet which is well-suited for data with fractal properties. Garbor wavelets or opponent
processes are frequently found in any biological functions.
|