One-Dimensional Discrete Wavelet Analysis :: Using Wavelets (Wavelet Toolbox)

Wavelet Toolbox

One-Dimensional Discrete Wavelet Analysis

This section takes you through the features of one-dimensional discrete wavelet analysis using the MATLAB Wavelet Toolbox.

The Wavelet Toolbox provides these functions for one-dimensional signal analysis. For more information, see the reference pages.

Analysis-Decomposition Functions

Function Name
Purpose

dwt
Single-level decomposition

wavedec
Decomposition

wmaxlev
Maximum wavelet decomposition level

Function Name	Purpose
`dwt`	Single-level decomposition
`wavedec`	Decomposition
`wmaxlev`	Maximum wavelet decomposition level

Synthesis-Reconstruction Functions

Function Name
Purpose

idwt
Single-level reconstruction

waverec
Full reconstruction

wrcoef
Selective reconstruction

upcoef
Single reconstruction

Function Name	Purpose
`idwt`	Single-level reconstruction
`waverec`	Full reconstruction
`wrcoef`	Selective reconstruction
`upcoef`	Single reconstruction

Decomposition Structure Utilities

Function Name
Purpose

detcoef
Extraction of detail coefficients

appcoef
Extraction of approximation coefficients

upwlev
Recomposition of decomposition structure

Function Name	Purpose
`detcoef`	Extraction of detail coefficients
`appcoef`	Extraction of approximation coefficients
`upwlev`	Recomposition of decomposition structure

De-noising and Compression

Function Name
Purpose

ddencmp
Provide default values for de-noising and compression

wbmpen
Penalized threshold for wavelet 1-D or 2-D de-noising

wdcbm
Thresholds for wavelet 1-D using Birgé-Massart strategy

wdencmp
Wavelet de-noising and compression

wden
Automatic wavelet de-noising

wthrmngr
Threshold settings manager

Function Name	Purpose
`ddencmp`	Provide default values for de-noising and compression
`wbmpen`	Penalized threshold for wavelet 1-D or 2-D de-noising
`wdcbm`	Thresholds for wavelet 1-D using Birgé-Massart strategy
`wdencmp`	Wavelet de-noising and compression
`wden`	Automatic wavelet de-noising
`wthrmngr`	Threshold settings manager

In this section, you'll learn how to

Load a signal
Perform a single-level wavelet decomposition of a signal
Construct approximations and details from the coefficients
Display the approximation and detail
Regenerate a signal by inverse wavelet transform
Perform a multilevel wavelet decomposition of a signal
Extract approximation and detail coefficients
Reconstruct the level 3 approximation
Reconstruct the level 1, 2, and 3 details
Display the results of a multilevel decomposition
Reconstruct the original signal from the level 3 decomposition
Remove noise from a signal
Refine an analysis
Compress a signal
Show a signal's statistics and histograms

Since you can perform analyses either from the command line or using the graphical interface tools, this section has subsections covering each method.

The final subsection discusses how to exchange signal and coefficient information between the disk and the graphical tools.

Importing and Exporting Information from the Graphical Interface One-Dimensional Analysis Using the Command Line