Approximating Continuous Functions with Haar Approximations
Approximating Continuous Functions with Haar Approximations
The Haar scaling function is defined by
ϕ(x)=
|
|
On the Haar space is spanned by , where is a non-negative integer. A continuous function can be approximated by a piecewise constant function by projection into Haar space.
[0,1)
V
j
ϕ(x),ϕ(x-1),…,ϕ(x-(-1))
j/2
2
j
2
j/2
2
j
2
j/2
2
j
2
j
2
j