Wavelet Toolbox

Index

A

adding a new wavelet

algorithms

Coifman-Wickerhauser

decomposition

discrete wavelet transform (DWT)

fast wavelet transform (FWT)

stationary wavelet transform (SWT)

analysis

continuous

continuous or discrete

one-dimensional discrete wavelet

one-dimensional wavelet packet

analysis (continued)

orthogonal

time-scale

compared to other views

using redundant representation instead

translation invariant

two-dimensional discrete wavelet

two-dimensional wavelet packet

wavelet

wavelet packet

B

bases

See analysis,wavelet packets

besttree function

binning

density estimation

processed data

regression estimation

biorthogonal wavelets

definition

presentation

C

calculating a default global threshold

centfrq function

chirp signal

example analysis

coefficients

approximation

extracting one-dimensional

fast wavelet transform

coloration

complex continuous wavelet

continuous wavelet

detail

fast wavelet transform

discrete wavelet

load

See importing to the GUI

save

See exporting from the GUI

coiflets

Coloration Mode

controlling the colormap

Coloration Mode menu

colored AR(3) noise example

complex frequency B-spline wavelets

complex Gaussian wavelets

complex Morlet wavelets

complex Shannon wavelets

compressing images

fingerprint example

using graphical interface

compression

ddencmp function

difference with de-noising

predefined strategies

procedure

wavelet packets

wavelets

retained energy

thresholding strategies

using wavelet packets

continuous wavelet transform (CWT)

creating

definition

difference from discrete wavelet transform

D

Daubechies wavelets

decimation

decomposition

displaying results of multilevel

decomposition (continued)

entropy-based criteria

hierarchical organization

load

See importing to the GUI

multistep

optical comparison

performing multilevel

using command line

using graphical interface

save

See exporting from the GUI

single-level

structure

one-dimensional

two-dimensional

wavelet decomposition tree

de-noising

basic model

graphical interface tools option

predefined strategies

procedure

de-noising (continued)

using SWT

1-D using command line

1-D using graphical interface

2-D analysis example

2-D using graphical interface

using thresholding

variance adaptive

white noise

de-noising images

2-D wavelet analysis and 2-D stationary wavelet analysis

stationary wavelet transform

two-dimensional procedure

de-noising signals

process

wavelet analysis

density estimation

definition

one-dimensional wavelet

details

coefficients

extracting one-dimensional

extracting two-dimensional

decomposition

definition

mathematical definition

reconstruction

wavelet decomposition

dilation equation

twin-scale relation

discontinuities

detecting

E

edge effects

See border distortion

entropy

criterion to select the best decomposition

definitions

estimation

default values

F

fast multiplication of large matrices

fast wavelet transform (FWT)

See transforms

filters

FIR

biorthogonal case

M-file used for construction

high-pass

low-pass

minimum phase

filters (continued)

quadrature mirror

G

Gaussian wavelets

GUI

complex continuous wavelet

continuous wavelet

density estimation

full window resolution

image de-noising using SWT

image extension / truncation

local variance adaptive thresholding

regression estimation

signal de-noising using SWT

signal extension / truncation

using menus

using the mouse

wavelet coefficients selection 1-D

wavelet coefficients selection 2-D

wavelet display

wavelet one-dimensional

wavelet packet

wavelet packet display

wavelet two-dimensional

H

Haar wavelet

definition

presentation

Heisenberg uncertainty principle

I

IDWT

See inverse discrete wavelet transform, transforms

images

indexed

importing to the GUI

complex continuous wavelet

continuous wavelet

discrete stationary wavelet 1-D

discrete stationary wavelet 2-D

discrete wavelet 2-D

variance adaptive thresholding

wavelet 1-D

wavelet density estimation 1-D

wavelet packets

wavelet regression estimation 1-D

indexed images

image matrix

matrix indices

shifting up

inverse discrete wavelet transform (IDWT)

inverse stationary wavelet transform (ISWT)

ISWT

See inverse stationary wavelet, transforms

iswt command

iswt2 command

L

level

decomposition

M

merge

Mexican hat wavelet

Meyer wavelet

M-files

More Display Options button

More on Residuals for Wavelet 1-D Compression window

Morlet wavelet

N

node

noise

noise (continued)

removing using GUI option

suppressing

O

objects

orthogonal wavelets

outliers

suppressing

P

packets

See wavelet packets

padding

See border distortion

periodic-padding

signal extension

periodized wavelet transform

See border distortion

polynomial + white noise example

positions

predefined wavelet families

Q

quadrature mirror filters (QMF)

and scaling function

creating the waveform

orthfilt function

system

R

ramp + colored noise example

ramp + white noise example

random design

See regression estimation

real electricity consumption signal example

reconstruction

regression estimation

goal

one-dimensional wavelet

regularity

definition

wavelet families

resemblance index

residuals display

1-D discrete wavelet compression

1-D stationary wavelet decomposition

2-D discrete wavelet compression

2-D stationary wavelet decomposition

reverse biorthogonal wavelets

RGB images

colormap matrix

converting from

S

save

See exporting from the GUI

scal2frq function

scale

and frequency

choosing using command line

choosing using graphical interface

dyadic

to frequency

scaling filters

scaling functions

second-derivative discontinuity example

self-similarity

T

thresholding

for optimal de-noising

rules

U

uniform white noise example

upsampling

two-dimensional IDWT

wavelet reconstruction process

V

vanishing moments

suppression of signals

wavelet families

variance adaptive thresholding

view axes

W

Wavelet 1-D De-Noising window

Wavelet 2-D Compression window

Wavelet 2-D tool

fingerprint example

wavelet analysis

advantage over Fourier

as Fourier-type function

de-noising signals

revealing signal trends

wavelet families

regularity

wavelet filters

wavelet notation

Wavelet Packet 1-D Compression window

Wavelet Packet 1-D menu item

Wavelet Packet 1-D tool

starting

Wavelet Packet 2-D Compression window

wavelet packets

analysis

and wavelet analysis

best level decomposition

computing the best tree

decomposition tree

de-noising

wavelet packets (continued)

selecting threshold for compression

tree

wavelets

biorthogonal

coiflets

complex frequency B-spline

Daubechies

Haar

wavelets (continued)

Mexican hat

Meyer

Morlet

one-dimensional analysis

one-dimensional capabilities

objects

table

organization

relationship of filters to

symlets

Z

zero-padding

signal extension

zoom

Example 4: Building a Wavelet Tree Object (EDWTTREE)