2.11.2.5 idwt(Pro)

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

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

More Information

For more information, please refer to our User Guide.


Related X-Functions

dwt, dwt2, idwt2


Keywords:wavelet, approximation