naginterfaces.library.wav.dim1_​mxolap_​fwd

naginterfaces.library.wav.dim1_mxolap_fwd(x, comm)

dim1_mxolap_fwd computes the one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function dim1_init() must be called first to set up the MODWT options.

For full information please refer to the NAG Library document for c09da

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/c09/c09daf.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 $6$)

On entry, the initialization function dim1_init() has not been called first or it has not been called with $wtrans=\text{‘T'}$, or the communication array $comm$[‘icomm’] has become corrupted.

Notes

dim1_mxolap_fwd computes the one-dimensional MODWT 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 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. Periodic (circular) convolution is available as an end extension method for application to finite data sets. The number $n_c$, of coefficients $C_a$ or $C_d$ is returned by the initialization function dim1_init().

References

Percival, D B and Walden, A T, 2000, Wavelet Methods for Time Series Analysis, Cambridge University Press