nag_imodwt (c09dbc) (PDF version)
c09 Chapter Contents
c09 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_imodwt (c09dbc)

+ Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

nag_imodwt (c09dbc) computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function nag_wfilt (c09aac) must be called first to set up the MODWT options.

2  Specification

#include <nag.h>
#include <nagc09.h>
void  nag_imodwt (Integer lenc, const double ca[], const double cd[], Integer n, double y[], const Integer icomm[], NagError *fail)

3  Description

nag_imodwt (c09dbc) performs the inverse operation of nag_modwt (c09dac). That is, given sets of nc approximation coefficients and detail coefficients, computed by nag_modwt (c09dac) using a MODWT as set up by the initialization function nag_wfilt (c09aac), on a real data array of length n, nag_imodwt (c09dbc) will reconstruct the data array yi, for i=1,2,,n, from which the coefficients were derived.

4  References

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

5  Arguments

1:     lencIntegerInput
On entry: the dimension of the arrays ca and cd.
Constraint: lencnc, where nc is the value returned in nwc by the call to the initialization function nag_wfilt (c09aac).
2:     ca[lenc]const doubleInput
On entry: the nc approximation coefficients, Ca. These will normally be the result of some transformation on the coefficients computed by nag_modwt (c09dac).
3:     cd[lenc]const doubleInput
On entry: the nc detail coefficients, Cd. These will normally be the result of some transformation on the coefficients computed by nag_modwt (c09dac).
4:     nIntegerInput
On entry: n, the length of the original data array from which the wavelet coefficients were computed by nag_modwt (c09dac) and the length of the data array y that is to be reconstructed by this function.
Constraint: This must be the same as the value n passed to the initialization function nag_wfilt (c09aac).
5:     y[n]doubleOutput
On exit: the reconstructed data based on approximation and detail coefficients Ca and Cd and the transform options supplied to the initialization function nag_wfilt (c09aac).
6:     icomm[100]const IntegerCommunication Array
On entry: contains details of the discrete wavelet transform and the problem dimension and, possibly, additional information on the previously computed forward transform.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ARRAY_DIM_LEN
On entry, array dimension lenc not large enough: lenc=value but must be at least value.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INITIALIZATION
On entry, n is inconsistent with the value passed to the initialization function: n=value, n should be value.
On entry, the initialization function nag_wfilt (c09aac) has not been called first or it has not been called with wtrans=Nag_MODWTSingle, or the communication array icomm has become corrupted.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

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.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

See Section 10 in nag_modwt (c09dac).

nag_imodwt (c09dbc) (PDF version)
c09 Chapter Contents
c09 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014