c09cac computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization function c09aac must be called first to set up the DWT options.

2 Specification

#include <nag.h>

void	c09cac (Integer n, const double x[], Integer lenc, double ca[], double cd[], Integer icomm[], NagError *fail)

The function may be called by the names: c09cac, nag_wav_dim1_sngl_fwd or nag_dwt.

3 Description

c09cac computes the one-dimensional DWT of a given input data array,

x_{i}

, for

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}

C_{d}

is returned by the initialization function c09aac.

4 References

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

5 Arguments

1: $n$ – Integer Input: On entry: the number of elements, $n$ , in the data array $x$ .

Constraint: this must be the same as the value n passed to the initialization function c09aac.
2: $x [n]$ – const double Input: On entry: x contains the input dataset $x_{i}$ , for $i = 1, 2, \dots, n$ .
3: $lenc$ – Integer Input: On entry: the dimension of the arrays ca and cd. This must be at least the number, $n_{c}$ , of approximation coefficients, $C_{a}$ , and detail coefficients, $C_{d}$ , of the discrete wavelet transform as returned in nwc by the call to the initialization function c09aac.

Constraint: $lenc \geq n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization function c09aac.
4: $ca [lenc]$ – double Output: On exit: $ca [i - 1]$ contains the $i$ th approximation coefficient, $C_{a} (i)$ , for $i = 1, 2, \dots, n_{c}$ .
5: $cd [lenc]$ – double Output: On exit: $cd [i - 1]$ contains the $i$ th detail coefficient, $C_{d} (i)$ , for $i = 1, 2, \dots, n_{c}$ .
6: $icomm [100]$ – Integer Communication Array: On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09aac.

On exit: contains additional information on the computed transform.
7: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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: Either the initialization function has not been called first or array icomm has been corrupted.

Either the initialization function was called with $wtrans = Nag_MultiLevel$ or array icomm has been corrupted.

On entry, n is inconsistent with the value passed to the initialization function: $n = ⟨ value ⟩$ , n should be $⟨ value ⟩$ .
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

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

c09cac is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example computes the one-dimensional discrete wavelet decomposition for

8

values using the Daubechies wavelet,

wavnam = Nag_Daubechies4

, with zero end extension.

c09ca: FL CL CPP AD

NAG CL Interfacec09cac (dim1_​sngl_​fwd)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
c09cac (dim1_sngl_fwd)