Haar wavelet
The
Haar wavelet is the first known
wavelet and was proposed in 1909 by Alfred Haar.
Note that the term
wavelet was coined much later.
The Haar wavelet is also the simplest possible wavelet.
It looks like that:
|
√1/2 ****O
|
|
0 *****O-------****
|
|
-√1/2 | ****O
0 1/2 1
The disadvantage of the Haar wavelet is that it is not
continuous and therefore not
differentiable.
The Haar Wavelet can also be described as a step function f(x) with:
- f(x) = 1 (if 0 <= x < 1/2)
- f(x) = -1 (if 1/2 <= x < 1)