Spectral Transformations - Biomedical Signal Analysis: Contemporary Methods and Applications - page 54

ψ

(t)

ψ ψ

0, 0 (t) =

(t) 0,n

n+1

1

t

0

n

1/2

ψ

(t)

ψ

(t) 1,n

1,0

2n+2

t

0 1 2 2n

Figure 2.10
Typical Haar wavelet for the scales 0 and 1.

We can easily show that

1
√ 2 [ ϕ m,2n + ϕ m,2n+1 ]

ϕ m+1,n =

and

1
√ 2 [ ϕ m,2n −

ψ m+1,n = ϕ m,2n+1 ] . (2.65)

Figure 2.10 illustrates a typical Haar wavelet for the scales 0 and 1.
Figure 2.11 shows the approximations P 0 f , P −1 f and the detail Q 0 f for
a function f . As stated in the context of multiresolution, the detail Q 0 f
is added to the coarser approximation P 0 f in order to obtain the finer