Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Scaling and Wavelet Filter

`Y = qmf(`

* X*,

`P`

Y = qmf(

`X`

Y = qmf(X,0)

`Y = qmf(`

changes the signs of the even index elements of the reversed vector filter
coefficients * X*,

`P`

`X`

`P`

`0`

. If `P`

`1`

, the signs of the odd index elements are
reversed. Changing `P`

changes the phase of the Fourier
transform of the resulting wavelet filter by π radians.`Y = qmf(`

is
equivalent to * X*)

`Y = qmf(X,0)`

. Let `x`

be a finite energy signal. Two filters *F _{0}* and

$${\Vert {y}_{0}\Vert}^{2}+{\Vert {y}_{1}\Vert}^{2}={\Vert x\Vert}^{2}$$

where *y _{0}* is a decimated
version of the signal

For example, if *F _{0}* is a Daubechies scaling filter
with norm equal to 1 and

`qmf`

(`db10`

):$$|{F}_{0}(z){|}^{2}+|{F}_{1}(z){|}^{2}=2.$$

Strang, G.; T. Nguyen (1996), *Wavelets and Filter
Banks*, Wellesley-Cambridge Press.

Was this topic helpful?