nag_wav_1d_mxolap_inv (c09db) computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function nag_wav_1d_init (c09aa) must be called first to set up the MODWT options.

Syntax

[y, ifail] = c09db(ca, cd, n, icomm, 'lenc', lenc)

[y, ifail] = nag_wav_1d_mxolap_inv(ca, cd, n, icomm, 'lenc', lenc)

Description

nag_wav_1d_mxolap_inv (c09db) performs the inverse operation of nag_wav_1d_mxolap_fwd (c09da). That is, given sets of

n_{c}

approximation coefficients and detail coefficients, computed by nag_wav_1d_mxolap_fwd (c09da) using a MODWT as set up by the initialization function nag_wav_1d_init (c09aa), on a real data array of length

n

, nag_wav_1d_mxolap_inv (c09db) will reconstruct the data array

y_{i}

, for

i = 1, 2, \dots, n

, from which the coefficients were derived.

References

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

Parameters

Compulsory Input Parameters

1: $ca (lenc)$ – double array: The $n_{c}$ approximation coefficients, $C_{a}$ . These will normally be the result of some transformation on the coefficients computed by nag_wav_1d_mxolap_fwd (c09da).
2: $cd (lenc)$ – double array: The $n_{c}$ detail coefficients, $C_{d}$ . These will normally be the result of some transformation on the coefficients computed by nag_wav_1d_mxolap_fwd (c09da).
3: $n$ – int64int32nag_int scalar: $n$ , the length of the original data array from which the wavelet coefficients were computed by nag_wav_1d_mxolap_fwd (c09da) 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_wav_1d_init (c09aa).
4: $icomm (100)$ – int64int32nag_int array: Contains details of the discrete wavelet transform and the problem dimension and, possibly, additional information on the previously computed forward transform.

Optional Input Parameters

1: $lenc$ – int64int32nag_int scalar: Default: the dimension of the arrays ca, cd. (An error is raised if these dimensions are not equal.)
The dimension of the arrays ca and cd.

Constraint: $lenc \geq n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization function nag_wav_1d_init (c09aa).

Output Parameters

1: $y (n)$ – double array: The reconstructed data based on approximation and detail coefficients $C_{a}$ and $C_{d}$ and the transform options supplied to the initialization function nag_wav_1d_init (c09aa).
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: On entry, array dimension lenc not large enough.

$ifail = 4$: On entry, n is inconsistent with the value passed to the initialization function.

$ifail = 6$: On entry, the initialization function nag_wav_1d_init (c09aa) has not been called first or it has not been called with $wtrans ='T'$ , or the communication array icomm has become corrupted.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

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.

Further Comments

None.

Example

See Example in nag_wav_1d_mxolap_fwd (c09da).

Open in the MATLAB editor: c09db_example

function c09db_example


fprintf('c09db example results\n\n');

% 1d maximal overlap discrete wavelet decomposition using a Daubechies wavelet

n      = int64(8);
x      = [1 3 5 7 6 4 5 2];

wavnam = 'DB4';
mode   = 'Periodic';
wtrans = 'Time invariant';

% Setup for wavelet
[nwlmax, nf, nwc, icomm, ifail] = c09aa(wavnam, wtrans, mode, n);

% Compute decomposition
[ca, cd, icomm, ifail] = c09da(x, nwc, icomm);

disp('Approximation coefficients:')
fprintf('%8.4f',ca);
fprintf('\n');
disp('Detail coefficients:')
fprintf('%8.4f',cd);
fprintf('\n');

% Reconstruct
[y, ifail] = c09db(ca, cd, n, icomm);
disp('Reconstruction:')
fprintf('%8.4f',y);
fprintf('\n');

c09db example results

Approximation coefficients:
  2.7781  1.5146  2.2505  4.8788  6.6845  6.3423  4.7869  3.7644
Detail coefficients:
 -0.6187  0.6272  0.1883 -1.1966  1.2618  0.3354 -0.3314 -0.2660
Reconstruction:
  1.0000  3.0000  5.0000  7.0000  6.0000  4.0000  5.0000  2.0000

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox