nag_dwt (c09cac) computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization function
nag_wfilt (c09aac) must be called first to set up the DWT options.
nag_dwt (c09cac) 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 function
nag_wfilt (c09aac).
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.