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orthfilt

Orthogonal wavelet filter set

Syntax

Description

[Lo_D,Hi_D,Lo_R,Hi_R] = orthfilt(W) computes the four filters associated with the scaling filter W corresponding to a wavelet:

Lo_D
Decomposition low-pass filter
Hi_D
Decomposition high-pass filter
Lo_R
Reconstruction low-pass filter
Hi_R
Reconstruction high-pass filter

For an orthogonal wavelet, in the multiresolution framework, we start with the scaling function phi and the wavelet function psi. One of the fundamental relations is the twin-scale relation:

All the filters used in dwt and idwt are intimately related to the sequence . Clearly if phi is compactly supported, the sequence (wn) is finite and can be viewed as a FIR filter. The scaling filter W is

For example, for the db3 scaling filter,

From filter W, we define four FIR filters, of length 2N and norm 1, organized as follows:

Filters
Low-Pass
High-Pass
Decomposition
Lo_D
Hi_D
Reconstruction
Lo_R
Hi_R

The four filters are computed using the following scheme:

where qmf is such that Hi_R and Lo_R are quadrature mirror filters
(i.e., Hi_R(k) = (-1)k Lo_R(2N + 1 - k), for k = 1, 2, ... , 2N), and where wrev flips the filter coefficients. So Hi_D and Lo_D are also quadrature mirror filters. The computation of these filters is performed using orthfilt.

Examples

See Also
biorfilt, qmf, wfilters

References

Daubechies I. (1992), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics. SIAM Ed. pp. 117-119, 137, 152.


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