C09EAF computes the two-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine
C09ABF must be called first to set up the DWT options.
C09EAF computes the two-dimensional DWT of a given input data array, considered as a matrix
$A$, at a single level. For a chosen wavelet filter pair, the output coefficients are obtained by applying convolution and downsampling by two to the input,
$A$, first over columns and then to the result over rows. The matrix of approximation (or smooth) coefficients,
${C}_{a}$, is produced by the low pass filter over columns and rows; the matrix of horizontal coefficients,
${C}_{h}$, is produced by the high pass filter over columns and the low pass filter over rows; the matrix of vertical coefficients,
${C}_{v}$, is produced by the low pass filter over columns and the high pass filter over rows; and the matrix of diagonal coefficients,
${C}_{d}$, is produced by the high pass filter over columns and rows. To reduce distortion effects at the ends of the data array, several end extension methods are commonly used. Those provided are: periodic or circular convolution end extension, half-point symmetric end extension, whole-point symmetric end extension and zero end extension. The total number,
${n}_{\mathrm{ct}}$, of coefficients computed for
${C}_{a}$,
${C}_{h}$,
${C}_{v}$, and
${C}_{d}$ together and the number of columns of each coefficients matrix,
${n}_{\mathrm{cn}}$, are returned by the initialization routine
C09ABF. These values can be used to calculate the number of rows of each coefficients matrix,
${n}_{\mathrm{cm}}$, using the formula
${n}_{\mathrm{cm}}={n}_{\mathrm{ct}}/\left(4{n}_{\mathrm{cn}}\right)$.
If on entry
${\mathbf{IFAIL}}={\mathbf{0}}$ or
${-{\mathbf{1}}}$, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The accuracy of the wavelet transform depends only on the floating point operations used in the convolution and downsampling and should thus be close to machine precision.
None.