naginterfaces.library.wav.dim1_​sngl_​fwd

naginterfaces.library.wav.dim1_sngl_fwd(x, comm)

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://support.nag.com/numeric/nl/nagdoc_30/flhtml/c09/c09caf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

$x$ contains the input dataset $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

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 $(:)$

$ca[i-1]$ contains the $i$th approximation coefficient, $C_a\left(\text{i}\right)$, for $\text{i}=1,2,\dots ,n_c$.

cdfloat, ndarray, shape $(:)$

$cd[\text{i}-1]$ contains the $\text{i}$th detail coefficient, $C_d\left(\text{i}\right)$, for $\text{i}=1,2,\dots ,n_c$.

Raises

NagValueError

(errno $1$)

On entry, $\text{n}$ is inconsistent with the value passed to the initialization function: $n=⟨value⟩$, $\text{n}$ should be $⟨value⟩$.

(errno $6$)

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

(errno $6$)

Either the initialization function was called with $wtrans=\text{‘M'}$ or array $comm$[‘icomm’] has been corrupted.

Notes

dim1_sngl_fwd computes the one-dimensional DWT of a given input data array, $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$, 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 dim1_init().

References

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