c09ca computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization method C09 Communication class constructor must be called first to set up the DWT options.

Syntax

C#
public static void c09ca( int n, double[] x, double[] ca, double[] cd, C09..::..C09Communications communications, out int ifail )

Visual Basic
Public Shared Sub c09ca ( _ n As Integer, _ x As Double(), _ ca As Double(), _ cd As Double(), _ communications As C09..::..C09Communications, _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void c09ca( int n, array<double>^ x, array<double>^ ca, array<double>^ cd, C09..::..C09Communications^ communications, [OutAttribute] int% ifail )

F#
static member c09ca : n : int * x : float[] * ca : float[] * cd : float[] * communications : C09..::..C09Communications * ifail : int byref -> unit

Parameters

n: Type: System..::..Int32
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 method c09aa.

x: Type: array<System..::..Double>[]()[][]
An array of size [n]
On entry: x contains the input dataset $x_{i}$ , for $i = 1, 2, \dots, n$ .

ca: Type: array<System..::..Double>[]()[][]
An array of size [lenc]
On exit: $ca [i - 1]$ contains the $i$ th approximation coefficient, $C_{a} (i)$ , for $i = 1, 2, \dots, n_{c}$ .

cd: Type: array<System..::..Double>[]()[][]
An array of size [lenc]
On exit: $cd [i - 1]$ contains the $i$ th detail coefficient, $C_{d} (i)$ , for $i = 1, 2, \dots, n_{c}$ .

communications: Type: NagLibrary..::..C09..::..C09Communications
An Object of type C09.c09caCommunications.

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

c09ca 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 method C09 Communication class constructor.

References

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

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$: On entry, n is inconsistent with the value passed to the initialization method C09 Communication class constructor.

$ifail = 2$: On entry, $lenc < n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization method C09 Communication class constructor.

$ifail = 6$: On entry, the initialization method C09 Communication class constructor has not been called first or it has been called with $wtrans = "M"$ , or the communication array icomm has become corrupted.

$ifail = -9000$: An error occured, see message report.
$ifail = -1000$: The array lengths are not the same for arrays
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

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.