2.11.2.1 cw_evaluate(Pro)

Brief Information

Compute values of a chosen wavelet at specified evaluation points

Additional Information

This feature is for OriginPro only.

Command Line Usage

1. cw_evaluate type:=dgauss param:=3 lb:=-8 ub:=8 npts:=200

2. cw_evaluate type:=morlet param:=8

3. cw_evaluate type:=maxhat npts:=50 oy:=(col(1), col(2))

Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Wavelet Type type

Input

int

morlet

Specify the type of wavelet.

Option list

  • morlet:Morlet
    The Morlet wavelet.
  • dgauss:DGauss
    The Derivative of a Gaussian wavelet.
  • mexhat:MexHat
    The Mexican Hat Wavelet.
Wave Number param

Input

int

5

If wavelet type is Morlet, this variable specifies the wave number, which should be not less than 5 and not larger than 20. If wavelet type is DGauss, this variable specifies the order of derivative, which should be a positive integer less than 9.

Lower Bound lb

Input

double

-10

Specify the lower bound of evaluation points

Upper Bound ub

Input

double

10

Specify the upper bound of evaluation points

Points of Wavelet Function npts

Input

int

100

Specify the number of evaluation points

Wavelet Function oy

Output

XYRange

<new>

Specify the output range

See the syntax here.

Description

This X-Function computes the values of the chosen wavelet at the supplied evaluation points. The number of evaluation points is specified by user. And the range of the evaluation points is determined by the lower bound and upper bound.

You can use this function to evaluate three wavelet types, including Morlet, Mexican Hat and the derivative of Gaussian wavelets. See below for their definition.

The Morlet wavelet is defined as:
Cw evaluate help English files image002.gif

where k is the wave number.

The Mexican Hat wavelet is:
Cw evaluate help English files image004.gif

And the Gaussian wavelet is the pth derivative of the Gaussian function, which is defined as:
Cw evaluate help English files image006.gif

where p is the derivative order.

Examples

1. To computes the values of Mexican Hat wavelet for 150 evaluation points range from -8 to 7, use the following script command:

cw_evaluate type:=2 lb:=-8 ub:=7 npts:=150

2. To change the wavelet type, you can either use the Type drop-down list in the dialog, which can be open by typing in the command Window:

cw_evaluate -d;

Or specify which type of wavelet to use from the script line by typing, for example

cw_evalute type:=1

Algorithm

The computation is implemented with three NAG functions: nag_morlet(), nag_dgauss() and nag_mexhat().

References

Torrence, C and Compo, G... 1998. A practical guide to wavelet analysis, Bull. Amer. Meteor. Soc.

Ingrid Daubechies. 1992. Ten Lectures On Wavelets. SIAM.

Related X-Functions

dwt, idwt