C09CAF computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine
C09AAF must be called first to set up the DWT options.
C09CAF computes the one-dimensional DWT of a given input data array,
${x}_{\mathit{i}}$, for
$\mathit{i}=1,2,\dots ,n$,
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,
$x$. The approximation (or smooth) coefficients,
${C}_{a}$, are produced by the low pass filter and the detail coefficients,
${C}_{d}$, by the high pass filter. 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 or zero end extension. The number
${n}_{c}$, of coefficients
${C}_{a}$ or
${C}_{d}$ is returned by the initialization routine
C09AAF.
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.