wfilters (Wavelet Toolbox)

Wavelet filters

Syntax

[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('wname')
[F1,F2] = wfilters('wname','type')

Description

[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('wname') computes four filters associated with the orthogonal or biorthogonal wavelet named in the string 'wname'.

The four output filters are

Lo_D, the decomposition low-pass filter
Hi_D, the decomposition high-pass filter
Lo_R, the reconstruction low-pass filter
Hi_R, the reconstruction high-pass filter

Available orthogonal or biorthogonal wavelet names 'wname' are listed in the table below.

Wavelet Families
Wavelets

Daubechies
'db1' or 'haar', 'db2', ... ,'db10', ... , 'db45'

Coiflets
'coif1', ... , 'coif5'

Symlets
'sym2', ... , 'sym8', ... ,'sym45'

Discrete Meyer
'dmey'

Biorthogonal
'bior1.1', 'bior1.3', 'bior1.5'
'bior2.2', 'bior2.4', 'bior2.6', 'bior2.8'
'bior3.1', 'bior3.3', 'bior3.5', 'bior3.7'
'bior3.9', 'bior4.4', 'bior5.5', 'bior6.8'

Reverse Biorthogonal
'rbio1.1', 'rbio1.3', 'rbio1.5'
'rbio2.2', 'rbio2.4', 'rbio2.6', 'rbio2.8'
'rbio3.1', 'rbio3.3', 'rbio3.5', 'rbio3.7'
'rbio3.9', 'rbio4.4', 'rbio5.5', 'rbio6.8'

Wavelet Families	Wavelets
`Daubechies`	'db1' or 'haar', 'db2', ... ,'db10', ... , 'db45'
`Coiflets`	'coif1', ... , 'coif5'
`Symlets`	'sym2', ... , 'sym8', ... ,'sym45'
`Discrete Meyer`	'dmey'
`Biorthogonal`	'bior1.1', 'bior1.3', 'bior1.5' 'bior2.2', 'bior2.4', 'bior2.6', 'bior2.8' 'bior3.1', 'bior3.3', 'bior3.5', 'bior3.7' 'bior3.9', 'bior4.4', 'bior5.5', 'bior6.8'
Reverse Biorthogonal	'rbio1.1', 'rbio1.3', 'rbio1.5' 'rbio2.2', 'rbio2.4', 'rbio2.6', 'rbio2.8' 'rbio3.1', 'rbio3.3', 'rbio3.5', 'rbio3.7' 'rbio3.9', 'rbio4.4', 'rbio5.5', 'rbio6.8'

[F1,F2] = wfilters('wname','type') returns the following filters:

Lo_D and Hi_D
(Decomposition filters)
If 'type' = 'd'

Lo_R and Hi_R
(Reconstruction filters)
If 'type' = 'r'

Lo_D and Lo_R
(Low-pass filters)
If 'type' = 'l'

Hi_D and Hi_R
(High-pass filters)
If 'type' = 'h'

`Lo_D` and `Hi_D`	(Decomposition filters)	If '`type`' = `'d'`
`Lo_R` and `Hi_R`	(Reconstruction filters)	If '`type`' = `'r'`
`Lo_D` and `Lo_R`	(Low-pass filters)	If '`type`' = `'l'`
`Hi_D` and `Hi_R`	(High-pass filters)	If '`type`' = `'h'`

Examples

% Set wavelet name. 
wname = 'db5';

% Compute the four filters associated with wavelet name given 
% by the input string wname. 
[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters(wname); 
subplot(221); stem(Lo_D); 
title('Decomposition low-pass filter'); 
subplot(222); stem(Hi_D); 
title('Decomposition high-pass filter'); 
subplot(223); stem(Lo_R); 
title('Reconstruction low-pass filter'); 
subplot(224); stem(Hi_R); 
title('Reconstruction high-pass filter'); 
xlabel('The four filters for db5')

% Editing some graphical properties,
% the following figure is generated.

See Also
biorfilt, orthfilt, waveinfo

References

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

Mallat, S. (1989), "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, pp. 674-693.

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