C09AAF returns the details of the chosen discrete wavelet filter. For a chosen mother wavelet, discrete wavelet transform type (single-level or multi-level DWT) and end extension method, this routine returns the number of levels of resolution (appropriate to a multi-level transform), the filter length, and, the number of approximation and detail coefficients, or the total number of coefficients (for single-level or multi-level DWTs respectively). This routine must be called before any of the transform routines in this chapter.
One-dimensional discrete wavelet transforms (DWT) are characterised by the mother wavelet, the end extension method and whether multiresolution analysis is to be performed. For the selected combination of choices for these three characteristics, and for a given length (
n) of data array, C09AAF returns the dimension details for the transform determined by this combination. The dimension details are:
nl, the number of levels of resolution that would be computed were a multi-level DWT applied,
nf, the filter length, and
nc the number of approximation and detail coefficients for single-level DWTs and the total number of coefficients for multi-level DWTs that would be generated by the transform. These values are also stored in the communication array
ICOMM, as are the input choices, so that they may be conveniently communicated to the transform routines in this chapter.
None.
- 1: WAVNAM – CHARACTER*(*)Input
On entry: the name of the mother wavelet. See the
C09 Chapter Introduction for details.
- WAVNAM='HAAR'
- Haar wavelet.
- WAVNAM='DBn', where n=2,3,…,10
- Daubechies wavelet with n vanishing moments (2n coefficients).
For example, WAVNAM='DB4' is the name for the Daubechies wavelet with 4 vanishing moments (8 coefficients).
- WAVNAM='BIORx.y', where x.y can be one of 1.1, 1.3, 1.5, 2.2, 2.4, 2.6, 2.8, 3.1, 3.3, 3.5 or 3.7
- Biorthogonal wavelet of order x.y. For example WAVNAM='BIOR3.1' is the name for the Biorthogonal wavelet of order 3.1.
Constraint:
WAVNAM='HAAR', 'DB2', 'DB3', 'DB4', 'DB5', 'DB6', 'DB7', 'DB8', 'DB9', 'DB10', 'BIOR1.1', 'BIOR1.3', 'BIOR1.5', 'BIOR2.2', 'BIOR2.4', 'BIOR2.6', 'BIOR2.8', 'BIOR3.1', 'BIOR3.3', 'BIOR3.5' or 'BIOR3.7'.
- 2: WTRANS – CHARACTER*1Input
On entry: the type of discrete wavelet transform that is to be applied.
- WTRANS='S'
- Single-level decomposition or reconstruction by discrete wavelet transform.
- WTRANS='M'
- Multi-level resolution, by a multi-level DWT or its inverse.
Constraint:
WTRANS='S' or 'M'.
- 3: MODE – CHARACTER*1Input
On entry: the end extension method.
- MODE='P'
- Periodic end extension.
- MODE='H'
- Half-point symmetric end extension.
- MODE='W'
- Whole-point symmetric end extension.
- MODE='Z'
- Zero end extension.
Constraints:
- if WTRANS='S', MODE='P', 'H', 'W' or 'Z';
- if WTRANS='M', MODE='H', 'W' or 'Z'.
- 4: N – INTEGERInput
On entry: the number of elements, n, in the data array x.
Constraint:
N≥2.
- 5: NWL – INTEGEROutput
-
On exit: the maximum number of levels of resolution, nl, that can be computed when a multi-level discrete wavelet transform is applied. It is such that 2nl≤n<2nl+1, for nl an integer.
- 6: NF – INTEGEROutput
On exit: the filter length, nf, for the supplied mother wavelet. This is used to determine the number of approximation coefficients that are appropriate to each level of a multi-level DWT.
- 7: NWC – INTEGEROutput
-
On exit: for a single-level transform (WTRANS='S'), the number of approximation coefficients that would be generated for the given problem size, mother wavelet, extension method and type of transform; this is also the corresponding number of detail coefficients. For a multi-level transform (WTRANS='M') the total number of coefficients that would be generated over all levels of resolution.
- 8: ICOMM(100) – INTEGER arrayCommunication Array
-
On exit: contains details of the wavelet transform and the problem dimension which is to be communicated to the discrete transform routines in this chapter.
- 9: IFAIL – INTEGERInput/Output
-
On entry:
IFAIL must be set to
0,
-1 or 1. If you are unfamiliar with this parameter you should refer to
Section 3.3 in the Essential Introduction for details.
On exit:
IFAIL=0 unless the routine detects an error (see
Section 6).
For environments where it might be inappropriate to halt program execution when an error is detected, the value
-1 or 1 is recommended. If the output of error messages is undesirable, then the value
1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
0.
When the value -1 or 1 is used it is essential to test the value of IFAIL on exit.
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable.
None.