wavemngr
Wavelet manager
Syntax
Description
Use wavemngr
to add, delete, restore, or read
wavelets.
wavemngr('add',
adds a wavelet family to the toolbox. These parameters define the wavelet family:FN
,FSN
,WT
,NUMS
,FILE
)
FN
— Family nameFSN
— Family short nameWT
— Wavelet family typeNUMS
— Wavelet parametersFILE
— Wavelet definition file
Note
When you use wavemngr
to add a wavelet family,
three wavelet extension files are created in the current folder: the two
ASCII files wavelets.asc
and
wavelets.prv
, and the MAT-file
wavelets.inf
. If you add a new wavelet family, it
is available in this folder only.
wavemngr('restore')
restores the previous
wavelets.asc
ASCII file
wavemngr('restore',IN2)
restores the initial
wavelets.asc
ASCII file. Here IN2
is a
dummy argument.
Examples
Wavelet Names and Family Names
List the wavelet families available by default.
wavemngr('read')
ans = 23x35 char array
'==================================='
'Haar ->->haar '
'Daubechies ->->db '
'Symlets ->->sym '
'Coiflets ->->coif '
'BiorSplines ->->bior '
'ReverseBior ->->rbio '
'Meyer ->->meyr '
'DMeyer ->->dmey '
'Gaussian ->->gaus '
'Mexican_hat ->->mexh '
'Morlet ->->morl '
'Complex Gaussian ->->cgau '
'Shannon ->->shan '
'Frequency B-Spline ->->fbsp '
'Complex Morlet ->->cmor '
'Fejer-Korovkin ->->fk '
'Best-localized Daubechies->->bl '
'Morris minimum-bandwidth ->->mb '
'Beylkin ->->beyl '
'Vaidyanathan ->->vaid '
'Han linear-phase moments ->->han '
'==================================='
List all wavelets.
wavemngr('read',1)
ans = 89x44 char array
'=================================== '
'Haar ->->haar '
'=================================== '
'Daubechies ->->db '
'------------------------------ '
'db1->db2->db3->db4-> '
'db5->db6->db7->db8-> '
'db9->db10->db**-> '
'=================================== '
'Symlets ->->sym '
'------------------------------ '
'sym2->sym3->sym4->sym5-> '
'sym6->sym7->sym8->sym**-> '
'=================================== '
'Coiflets ->->coif '
'------------------------------ '
'coif1->coif2->coif3->coif4-> '
'coif5-> '
'=================================== '
'BiorSplines ->->bior '
'------------------------------ '
'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-> '
'=================================== '
'ReverseBior ->->rbio '
'------------------------------ '
'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-> '
'=================================== '
'Meyer ->->meyr '
'=================================== '
'DMeyer ->->dmey '
'=================================== '
'Gaussian ->->gaus '
'------------------------------ '
'gaus1->gaus2->gaus3->gaus4-> '
'gaus5->gaus6->gaus7->gaus8-> '
'=================================== '
'Mexican_hat ->->mexh '
'=================================== '
'Morlet ->->morl '
'=================================== '
'Complex Gaussian ->->cgau '
'------------------------------ '
'cgau1->cgau2->cgau3->cgau4-> '
'cgau5->cgau6->cgau7->cgau8-> '
'=================================== '
'Shannon ->->shan '
'------------------------------ '
'shan1-1.5->shan1-1->shan1-0.5->shan1-0.1-> '
'shan2-3->shan**-> '
'=================================== '
'Frequency B-Spline ->->fbsp '
'------------------------------ '
'fbsp1-1-1.5->fbsp1-1-1->fbsp1-1-0.5->fbsp2-1-1->'
'fbsp2-1-0.5->fbsp2-1-0.1->fbsp**-> '
'=================================== '
'Complex Morlet ->->cmor '
'------------------------------ '
'cmor1-1.5->cmor1-1->cmor1-0.5->cmor1-1-> '
'cmor1-0.5->cmor1-0.1->cmor**-> '
'=================================== '
'Fejer-Korovkin ->->fk '
'------------------------------ '
'fk4->fk6->fk8->fk14-> '
'fk18->fk22-> '
'=================================== '
'Best-localized Daubechies->->bl '
'------------------------------ '
'bl7->bl9->bl10-> '
'=================================== '
'Morris minimum-bandwidth ->->mb '
'------------------------------ '
'mb4.2->mb8.2->mb8.3->mb8.4-> '
'mb10.3->mb12.3->mb14.3->mb16.3-> '
'mb18.3->mb24.3->mb32.3-> '
'=================================== '
'Beylkin ->->beyl '
'=================================== '
'Vaidyanathan ->->vaid '
'=================================== '
'Han linear-phase moments ->->han '
'------------------------------ '
'han2.3->han3.3->han4.5->han5.5-> '
'=================================== '
Add Wavelet Families
This example shows how to add new compactly supported orthogonal wavelets to the toolbox. These wavelets, which are a slight generalization of the Daubechies wavelets, are based on the use of Bernstein polynomials and are due to Kateb and Lemarié.
Add a new family of orthogonal wavelets. You must define:
Family Name:
Lemarie
Family Short Name:
lem
Type of wavelet:
1 (orth)
Wavelet numbers:
1 2 3 4 5
File driver:
lemwavf
The source code for lemwavf.m
is in the same folder as this example. The input argument of lemwavf
is a character vector of the form lem
N, where N = 1, 2, 3, 4, or 5.
wavemngr('add','Lemarie','lem',1,'1 2 3 4 5','lemwavf')
The ASCII file wavelets.asc
is saved as wavelets.prv
, then information defining the new family is added to wavelets.asc
, and the MAT-file wavelets.inf
is generated.
Note that wavemngr
works on the current folder. If you add a new wavelet family, it is available in this folder only.
List the available wavelet families. Confirm the new wavelet family is added.
wavemngr('read')
ans = 24x35 char array
'==================================='
'Haar ->->haar '
'Daubechies ->->db '
'Symlets ->->sym '
'Coiflets ->->coif '
'BiorSplines ->->bior '
'ReverseBior ->->rbio '
'Meyer ->->meyr '
'DMeyer ->->dmey '
'Gaussian ->->gaus '
'Mexican_hat ->->mexh '
'Morlet ->->morl '
'Complex Gaussian ->->cgau '
'Shannon ->->shan '
'Frequency B-Spline ->->fbsp '
'Complex Morlet ->->cmor '
'Fejer-Korovkin ->->fk '
'Best-localized Daubechies->->bl '
'Morris minimum-bandwidth ->->mb '
'Beylkin ->->beyl '
'Vaidyanathan ->->vaid '
'Han linear-phase moments ->->han '
'Lemarie ->->lem '
'==================================='
Remove the added family. Regenerate the list of wavelet families.
wavemngr('del','Lemarie') wavemngr('read')
ans = 23x35 char array
'==================================='
'Haar ->->haar '
'Daubechies ->->db '
'Symlets ->->sym '
'Coiflets ->->coif '
'BiorSplines ->->bior '
'ReverseBior ->->rbio '
'Meyer ->->meyr '
'DMeyer ->->dmey '
'Gaussian ->->gaus '
'Mexican_hat ->->mexh '
'Morlet ->->morl '
'Complex Gaussian ->->cgau '
'Shannon ->->shan '
'Frequency B-Spline ->->fbsp '
'Complex Morlet ->->cmor '
'Fejer-Korovkin ->->fk '
'Best-localized Daubechies->->bl '
'Morris minimum-bandwidth ->->mb '
'Beylkin ->->beyl '
'Vaidyanathan ->->vaid '
'Han linear-phase moments ->->han '
'==================================='
Restore the previous ASCII file wavelets.prv
, then build the MAT-file wavelets.inf
. List the restored wavelets. Because wavemngr
reads the ASCII file in the current working directory, the new family appears in the list.
wavemngr('restore') wavemngr('read',1)
ans = 94x44 char array
'=================================== '
'Haar ->->haar '
'=================================== '
'Daubechies ->->db '
'------------------------------ '
'db1->db2->db3->db4-> '
'db5->db6->db7->db8-> '
'db9->db10->db**-> '
'=================================== '
'Symlets ->->sym '
'------------------------------ '
'sym2->sym3->sym4->sym5-> '
'sym6->sym7->sym8->sym**-> '
'=================================== '
'Coiflets ->->coif '
'------------------------------ '
'coif1->coif2->coif3->coif4-> '
'coif5-> '
'=================================== '
'BiorSplines ->->bior '
'------------------------------ '
'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-> '
'=================================== '
'ReverseBior ->->rbio '
'------------------------------ '
'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-> '
'=================================== '
'Meyer ->->meyr '
'=================================== '
'DMeyer ->->dmey '
'=================================== '
'Gaussian ->->gaus '
'------------------------------ '
'gaus1->gaus2->gaus3->gaus4-> '
'gaus5->gaus6->gaus7->gaus8-> '
'=================================== '
'Mexican_hat ->->mexh '
'=================================== '
'Morlet ->->morl '
'=================================== '
'Complex Gaussian ->->cgau '
'------------------------------ '
'cgau1->cgau2->cgau3->cgau4-> '
'cgau5->cgau6->cgau7->cgau8-> '
'=================================== '
'Shannon ->->shan '
'------------------------------ '
'shan1-1.5->shan1-1->shan1-0.5->shan1-0.1-> '
'shan2-3->shan**-> '
'=================================== '
'Frequency B-Spline ->->fbsp '
'------------------------------ '
'fbsp1-1-1.5->fbsp1-1-1->fbsp1-1-0.5->fbsp2-1-1->'
'fbsp2-1-0.5->fbsp2-1-0.1->fbsp**-> '
'=================================== '
'Complex Morlet ->->cmor '
'------------------------------ '
'cmor1-1.5->cmor1-1->cmor1-0.5->cmor1-1-> '
'cmor1-0.5->cmor1-0.1->cmor**-> '
'=================================== '
'Fejer-Korovkin ->->fk '
'------------------------------ '
'fk4->fk6->fk8->fk14-> '
'fk18->fk22-> '
'=================================== '
'Best-localized Daubechies->->bl '
'------------------------------ '
'bl7->bl9->bl10-> '
'=================================== '
'Morris minimum-bandwidth ->->mb '
'------------------------------ '
'mb4.2->mb8.2->mb8.3->mb8.4-> '
'mb10.3->mb12.3->mb14.3->mb16.3-> '
'mb18.3->mb24.3->mb32.3-> '
'=================================== '
'Beylkin ->->beyl '
'=================================== '
'Vaidyanathan ->->vaid '
'=================================== '
'Han linear-phase moments ->->han '
'------------------------------ '
'han2.3->han3.3->han4.5->han5.5-> '
'=================================== '
'Lemarie ->->lem '
'------------------------------ '
'lem1->lem2->lem3->lem4-> '
'lem5-> '
'=================================== '
Restore the initial wavelets. Restore the initial ASCII file wavelets.ini
and the initial MAT-file wavelets.bin
. Regenerate the list of wavelet families. The list does not include the new family.
wavemngr('restore',0) wavemngr('read')
ans = 23x35 char array
'==================================='
'Haar ->->haar '
'Daubechies ->->db '
'Symlets ->->sym '
'Coiflets ->->coif '
'BiorSplines ->->bior '
'ReverseBior ->->rbio '
'Meyer ->->meyr '
'DMeyer ->->dmey '
'Gaussian ->->gaus '
'Mexican_hat ->->mexh '
'Morlet ->->morl '
'Complex Gaussian ->->cgau '
'Shannon ->->shan '
'Frequency B-Spline ->->fbsp '
'Complex Morlet ->->cmor '
'Fejer-Korovkin ->->fk '
'Best-localized Daubechies->->bl '
'Morris minimum-bandwidth ->->mb '
'Beylkin ->->beyl '
'Vaidyanathan ->->vaid '
'Han linear-phase moments ->->han '
'==================================='
All command line capabilities are available for new families of wavelets. Create a new family. Compute the four associated filters and the scale and wavelet functions.
wavemngr('add','Lemarie','lem',1,'1 2 3 4 5','lemwavf'); [Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('lem3'); [phi,psi,xval] = wavefun('lem3'); plot(xval,[phi;psi]); legend('Scaling Function','Wavelet') grid on
Remove the added family.
wavemngr('del','Lemarie')
Input Arguments
FN
— Wavelet family name
character vector | string scalar
Wavelet family name, specified as a character vector or string scalar.
FSN
— Wavelet family short name
character vector | string scalar
Wavelet family short name, specified as a character vector or string
scalar. The number of characters in FSN
must be less
than or equal to 4.
WT
— Wavelet family type
1
| 2
| 3
| 4
| 5
Wavelet family type, specified as one of the following:
1
— Orthogonal wavelets2
— Biorthogonal wavelets3
— Wavelet with a scaling function4
— Wavelet without a scaling function5
— Complex wavelet without a scaling function
NUMS
— Wavelet parameters
''
| character vector | string scalar
Wavelet parameters, specified as:
If the family consists of a single wavelet,
NUMS
is the empty string''
. For example, themexh
andmorl
families each contain a single wavelet.If the wavelet is member of a finite family of wavelets,
NUMS
contains a space-separated list of items representing wavelet parameters. For example, for the biorthogonal wavelet familybior
,NUMS = '1.1 1.3 1.5 2.2 2.4 2.6 2.8 3.1 3.3 3.5 3.7 3.9 4.4 5.5 6.8'
.If the wavelet is member of an infinite family of wavelets,
NUMS
contains a space-separated list of items representing wavelet parameters, terminated by the special sequence**
. Two examples are listed in the following table.Wavelet Family NUMS
db
NUMS = '1 2 3 4 5 6 7 8 9 10 **'
shan
NUMS = '1-1.5 1-1 1-0.5 1-0.1 2-3 **'
TYPNUMS
— Wavelet parameter input format
'integer'
(default) | 'real'
| 'charactervector'
Wavelet parameter input format, specified as:
'integer'
— Use this option when the parameter is an integer. For example, the Daubechies wavelet familydb
uses an integer parameter.'real'
— Use this option when the parameter is real. For example, the biorthogonal wavelet familybior
uses a real parameter.'charactervector'
— Use this option when the parameter is a character vector. For example, the Shannon wavelet family uses a character vector.
FILE
— Wavelet definition file
character vector | string scalar
Wavelet definition file, specified as a character vector or string scalar.
FILE
is the name of a MAT-file or a code file name
that defines the wavelet family.
If the wavelet family contains only one type 1 (orthogonal) or type 2 (biorthogonal) wavelet, you can define the wavelet in a MAT-file. The MAT-file contains the scaling filter coefficients. The filename must match the wavelet family short name.
If you define an orthogonal wavelet in a MAT-file, the name of the variable containing the scaling filter coefficients must match the name of the wavelet family short name.
If you define a biorthogonal wavelet in a MAT-file, the names of the variables containing the scaling filter coefficients must be
Df
andRf
.
For more information, see Add Quadrature Mirror and Biorthogonal Wavelet Filters.
Example: If a family that contains a single orthogonal wavelet has the
short name wfsn
, the variable wfsn
must contain the scaling filter coefficients. To create the necessary
MAT-file, you would use the command save wfsn
wfsn
.
B
— Effective support
two-element real-valued vector
Effective support for wavelets with family type WT
equal to 3, 4, or 5, specified as a two-element real-valued vector. If
B = [lb ub]
, then lb
specifies the
lower bound, and ub
specifies the upper bound.
Data Types: double
N
— Wavelet
character vector | string scalar
Wavelet or wavelet family to delete, specified by a character vector or
string scalar. N
is either the wavelet name or wavelet
family short name.
Example: wavemngr('del','Lemarie')
wname
— Wavelet
character vector | string scalar
Wavelet, specified as a character vector or string scalar. To learn what
wavelets are available in a wavelet family, use waveinfo
and the family
short name.
Example: ty = wavemngr('type',"coif4")
Output Arguments
out
— Wavelet manager output
character array
Wavelet manager output, returned as a character array.
wavetype
— Wavelet family type
integer
Wavelet family type, returned as an integer.
1
— Orthogonal wavelets2
— Biorthogonal wavelets3
— Wavelet with a scaling function4
— Wavelet without a scaling function5
— Complex wavelet without a scaling function
Limitations
wavemngr
allows you to add a wavelet. You must verify that it is truly a wavelet. No check is performed to confirm the addition is a wavelet or to confirm the type of the new wavelet. You can useisorthwfb
andisbiorthwfb
to determine if a wavelet is orthogonal or biorthogonal.
References
[1] Daubechies, I. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1992.
Version History
Introduced before R2006a
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