naginterfaces.library.wav.dim1_​sngl_​fwd

naginterfaces.library.wav.dim1_sngl_fwd(x, comm)[source]

dim1_sngl_fwd computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization function dim1_init() must be called first to set up the DWT options.

For full information please refer to the NAG Library document for c09ca

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/c09/c09caf.html

Parameters
xfloat, array-like, shape

contains the input dataset , for .

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by a prior call to dim1_init().

Returns
cafloat, ndarray, shape

contains the th approximation coefficient, , for .

cdfloat, ndarray, shape

contains the th detail coefficient, , for .

Raises
NagValueError
(errno )

On entry, is inconsistent with the value passed to the initialization function: , should be .

(errno )

Either the initialization function has not been called first or array [‘icomm’] has been corrupted.

(errno )

Either the initialization function was called with or array [‘icomm’] has been corrupted.

Notes

dim1_sngl_fwd computes the one-dimensional DWT of a given input data array, , for , 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, . The approximation (or smooth) coefficients, , are produced by the low pass filter and the detail coefficients, , 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 , of coefficients or is returned by the initialization function dim1_init().

References

Daubechies, I, 1992, Ten Lectures on Wavelets, SIAM, Philadelphia