Wavelet Toolbox

Build a MAT-File or M-File

The wavemngr command requires a file argument, which is a string containing a MAT-file or M-file name.

If a family contains many wavelets, a M-file must be defined and must be of a specific form that depends on the wavelet type. The specific M-file formats are described in the remainder of this section.

If a family contains a single wavelet, then a MAT-file can be defined for wavelets of type 1. It must have the wavelet family short name (fsn) argument as its name and must contain a single variable whose name is fsn and whose value is the scaling filter. An M-file can also be defined as discussed below.

Type 1 (Orthogonal with FIR Filter)

The syntax of the first line in the M-file must be:

function w = file(wname)

where the input argument wname is a string containing the wavelet name, and the output argument w is the corresponding scaling filter.

The filter w must be of even length otherwise it is zero-padded by the toolbox.

For predefined wavelets, the scaling filter is of sum 1. For a new wavelet, the normalization is free (except 0 of course) since the toolbox uses a suitably normalized version of this filter.

Examples of such M-files for predefined wavelets are: dbwavf.m for Daubechies, coifwavf.m for Coiflets, and symwavf.m for Symlets.

Type 2 (Biorthogonal with FIR Filter)

The syntax of the first line in the M-file must be:

function [wr,wd] = file(wname)

where the input argument wname is a string containing the wavelet name and the output arguments wr and wd are the corresponding reconstruction and decomposition scaling filters, respectively.

The filters wr and wd must be of the same even length. In general, initial biorthogonal filters do not meet these requirements, so they are zero-padded by the toolbox.

For predefined wavelets, the scaling filters are of sum 1. For a new wavelet, the normalization is free (except 0 of course) since the toolbox uses a suitably normalized version of these filters.

The M-file biorwavf.m (for BiorSplines) is an example of an M-file for a type-2 predefined wavelet family.

Type 3 (Orthogonal with Scale Function)

The syntax of the first line in the M-file must be:

function [phi,psi,t] = file(lb,ub,n,wname)

which returns values of the scaling function phi and of the wavelet function psi on t, a regular n-point grid of the interval [lb ub].

The argument wname is optional (see Note below).

The M-file meyer.m is an example of an M-file for a type-3 predefined wavelet family.

Type 4 or Type 5 (No FIR Filter; No Scale Function)

The syntax of the first line in the M-file must be:

function [psi,t] = file(lb,ub,n,wname)

or

function [psi,t] = file(lb,ub,n,wname, "additional arguments")

which returns values of the wavelet function psi on t, a regular n-point grid of the interval [lb ub].

The argument wname is optional (see Note below).

Examples of type-4 M-files for predefined wavelet families are mexihat.m (for Mexican_hat) and morlet.m (for Morlet).

Examples of type-5 M-files for predefined wavelet families are shanwavf.m (for Shannon) and cmorwavf.m (for Complex Morlet).

Note    For the types 3, 4, and 5, the wname argument can be optional. It is only required if the new wavelet family contains more than one wavelet and if you plan to use this new family in the GUI mode. For the types 4 and 5, a complete example of using the "additional arguments" can be found looking at the reference page for the fbspwavf function.

Define the Orders of Wavelets Within the Given Family

Define the Effective Support