2.11.2.5 idwt(Pro)

1 Menu Information
2 Brief Information
3 Additional Information
4 Command Line Usage
5 X-Function Execution Options
6 Variables
7 Description
8 Examples
9 More Information
10 Related X-Functions

Menu Information

Analysis: Signal Processing: Wavelet: Reconstruction

Brief Information

Reconstruct a signal from its coefficients

Additional Information

This feature is for OriginPro only.

Command Line Usage

1. idwt ca:=Col(1) cd:=Col(2); 
2. idwt ca:=Col(1) cd:=Col(2) ext:=z; 
3. idwt ca:=Col(1) cd:=Col(2) type:=db3; 
4. idwt ca:=Col(1) cd:=Col(2) ox:=Col(3); //coefficients in Column 1 and 2; save the result to Column 3

X-Function Execution Options

Please refer to the page for additional option switches when accessing the x-function from script

Variables

Display Name	Variable Name	I/O and Type	Default Value	Description
Approximation Coefficients	ca	Input vector	<active>	Specify the approximation coefficients
Detail Coefficients	cd	Input vector	<active>	Specify the detail coefficients
Wavelet Type	type	Input int	H	Specify the wavelet type. This should correspond to the wavelet type used by the wavelet decomposition that has produced the input coefficients. Option list haar:Haar Haar wavelet db 2:DB2 Daubechies wavelet (N=4 db 3:DB3 Daubechies wavelet (N=6) db 4:DB4 Daubechies wavelet (N=8) db 5:DB5 Daubechies wavelet (N=10) db 6:DB6 Daubechies wavelet (N=12) db 7:DB7 Daubechies wavelet (N=14) db 8:DB8 Daubechies wavelet (N=16) db 9:DB9 Daubechies wavelet (N=18) db 10:DB10 Daubechies wavelet (N=20) b11:Bior1.1 Biorthogonal (Nr=1, Nd=1) b13:Bior1.3 Biorthogonal (Nr=1, Nd=3) b15:Bior1.5 Biorthogonal (Nr=1, Nd=5) b22:Bior2.2 Biorthogonal (Nr=2, Nd=2) b24:Bior2.4 Biorthogonal (Nr=2, Nd=4) b26:Bior2.6 Biorthogonal (Nr=2, Nd=6) b28:Bior2.8 Biorthogonal (Nr=2, Nd=8) b31:Bior3.1 Biorthogonal (Nr=3, Nd=1) b33:Bior3.3 Biorthogonal (Nr=3 Nd=3) b35:Bior3.5 Biorthogonal (Nr=3, Nd=5) b37:Bior3.7 Biorthogonal (Nr=3, Nd=7)
Boundary	ext	Input int	P	Specify the end extension method to deal with boundary effects Option list periodic:Periodic The input signal will be viewed as periodic. z:Zero -padded The data points outside the input range will be viewed as zeroes.
Output	ox	Output vector	<new>	Specify the output signal

Description

idwt reconstructs a signal from its approximation coefficients and detail coefficients.

To construct the signal correctly, the wavelet type and the boundary should be the same with the options chosen for the decomposition that has produced the coefficients.

Examples

To reconstruct a signal from its approximation coefficients and detail coefficients saved in Column 1 and 2 of the active sheet using DB4 wavelet and periodic as the extension mode, use the Command Window:

idwt ca:=Col(1) cd:=Col(2) type:=1

To perform idwt using a pre-saved analysis theme called MyTheme, use the Command Window:

idwt -t "MyTheme"

Code Sample

// Wavelet decomposition and reconstruction with two different wavelet types
//Create a new workbook and import sample data
newbook  name:="Wavelet Demo" sheet:=1;
fname$=system.path.program$ + "Samples\Signal Processing\Step Signal With Random Noise.dat";
impasc;

//Multi-level wavelet decomposition using two wavelet types
mdwt ix:=col(2) type:=haar level:=3 rd:=[<input>]"Haar";
mdwt ix:=1!col(2) type:=db7 level:=3 rd:=[<input>]"DB7";
//Reconstruction
idwt ca:=2!1 cd:=2!2 type:=haar;
idwt ca:=2!5 cd:=2!3 type:=haar;
idwt ca:=2!6 cd:=2!4 type:=haar;
idwt ca:=3!1 cd:=3!2 type:=db2;
idwt ca:=3!5 cd:=3!3 type:=db2;
idwt ca:=3!6 cd:=3!4 type:=db2;

//Report
newsheet name:="report" labels:="|Haar|DB7";
wcolwidth irng:=1:3 width:="15";
wrowheight irng:=col(1)[1:5] height:=5;
wcellcolor irng:=col(1)[1:5] color:=color(249, 236, 151);
col(1)[1]$="CA3";
col(1)[2]$="CD3";
col(1)[3]$="CD2";
col(1)[4]$="CD1";
col(1)[5]$="Reconstructed";
//Insert sparklines for coefficients and reconstructed signals
insertSparklines irng:=(2!1:4, 2!7)  name:=0 orng:=col(2)[1];
insertSparklines irng:=(3!1:4, 3!7)  name:=0 orng:=col(3)[1];

window -z; //Maximize window