# lift::liftbase Class Reference

Inheritance diagram for lift::liftbase:

[legend]
List of all members.

## Public Member Functions

void forwardTrans (double[] vec)
void inverseTrans (double[] vec)

## Protected Member Functions

void split (double[] vec, int N)
void merge (double[] vec, int N)
abstract void predict (double[] vec, int N, int direction)
abstract void update (double[] vec, int N, int direction)

## Protected Attributes

final int forward = 1
final int inverse = 2

## Detailed Description

class liftbase: base class for simple Lifting Scheme wavelets using split, predict, update or update, predict, merge steps.

Simple lifting scheme wavelets consist of three steps, a split/merge step, predict step and an update step:

• The split step divides the elements in an array so that the even elements are in the first half and the odd elements are in the second half.

• The merge step is the inverse of the split step. It takes two regions of an array, an odd region and an even region and merges them into a new region where an even element alternates with an odd element.

• The predict step calculates the difference between an odd element and its predicted value based on the even elements. The difference between the predicted value and the actual value replaces the odd element.

• The predict step operates on the odd elements. The update step operates on the even element, replacing them with a difference between the predict value and the actual odd element. The update step replaces each even element with an average. The result of the update step becomes the input to the next recursive step in the wavelet calculation.

The split and merge methods are shared by all Lifting Scheme wavelet algorithms. This base class provides the transform and inverse transform methods (forwardTrans and inverseTrans). The predict and update methods are abstract and are defined for a particular Lifting Scheme wavelet sub-class.

References:

• The Wavelet Lifting Scheme by Ian Kaplan, www.bearcave.com. This is the parent web page for this Java source code.
• Ripples in Mathematics: the Discrete Wavelet Transform by Arne Jense and Anders la Cour-Harbo, Springer, 2001
• Building Your Own Wavelets at Home in Wavelets in Computer Graphics

#### Copyright and Use

You may use this source code without limitation and without fee as long as you include: <blockquote> This software was written and is copyrighted by Ian Kaplan, Bear Products International, www.bearcave.com, 2001. </blockquote>

This software is provided "as is", without any warrenty or claim as to its usefulness. Anyone who uses this source code uses it at their own risk. Nor is any support provided by Ian Kaplan and Bear Products International.

Please send any bug fixes or suggested source changes to:

```     iank@bearcave.com
```

Author:
Ian Kaplan

## Member Function Documentation

 void lift::liftbase::forwardTrans ( double[] vec ) ` [inline]`
 Simple wavelet Lifting Scheme forward transform forwardTrans is passed an array of doubles. The array size must be a power of two. Lifting Scheme wavelet transforms are calculated in-place and the result is returned in the argument array. The result of forwardTrans is a set of wavelet coefficients ordered by increasing frequency and an approximate average of the input data set in vec[0]. The coefficient bands follow this element in powers of two (e.g., 1, 2, 4, 8...). Reimplemented in lift::haarpoly, and lift::poly.```00206 { 00207 final int N = vec.length; 00208 00209 for (int n = N; n > 1; n = n >> 1) { 00210 split( vec, n ); 00211 predict( vec, n, forward ); 00212 update( vec, n, forward ); 00213 } 00214 } // forwardTrans ```

 void lift::liftbase::inverseTrans ( double[] vec ) ` [inline]`
 Default two step Lifting Scheme inverse wavelet transform inverseTrans is passed the result of an ordered wavelet transform, consisting of an average and a set of wavelet coefficients. The inverse transform is calculated in-place and the result is returned in the argument array. Reimplemented in lift::haarpoly, and lift::poly.```00232 { 00233 final int N = vec.length; 00234 00235 for (int n = 2; n <= N; n = n << 1) { 00236 update( vec, n, inverse ); 00237 predict( vec, n, inverse ); 00238 merge( vec, n ); 00239 } 00240 } // inverseTrans ```

 void lift::liftbase::merge ( double[] vec, int N ) ` [inline, protected]`
 Merge the odd elements from the second half of the N element region in the array with the even elements in the first half of the N element region. The result will be the combination of the odd and even elements in a region of length N. ```00149 { 00150 int half = N >> 1; 00151 int start = half-1; 00152 int end = half; 00153 00154 while (start > 0) { 00155 for (int i = start; i < end; i = i + 2) { 00156 double tmp = vec[i]; 00157 vec[i] = vec[i+1]; 00158 vec[i+1] = tmp; 00159 } 00160 start = start - 1; 00161 end = end + 1; 00162 } 00163 } ```

 abstract void lift::liftbase::predict ( double[] vec, int N, int direction ) ` [protected, pure virtual]`

Predict step, to be defined by the subclass

Parameters:
 vec input array N size of region to act on (from 0..N-1) direction forward or inverse transform

Implemented in lift::haar, lift::line, and lift::poly.

 void lift::liftbase::split ( double[] vec, int N ) ` [inline, protected]`
 Split the vec into even and odd elements, where the even elements are in the first half of the vector and the odd elements are in the second half. ```00124 { 00125 00126 int start = 1; 00127 int end = N - 1; 00128 00129 while (start < end) { 00130 for (int i = start; i < end; i = i + 2) { 00131 double tmp = vec[i]; 00132 vec[i] = vec[i+1]; 00133 vec[i+1] = tmp; 00134 } 00135 start = start + 1; 00136 end = end - 1; 00137 } 00138 } ```

 abstract void lift::liftbase::update ( double[] vec, int N, int direction ) ` [protected, pure virtual]`

Update step, to be defined by the subclass

Parameters:
 vec input array N size of region to act on (from 0..N-1) direction forward or inverse transform

Implemented in lift::haar, lift::line, and lift::poly.

## Member Data Documentation

 final int lift::liftbase::forward = 1` [protected]`
 "enumeration" for forward wavelet transform

 final int lift::liftbase::inverse = 2` [protected]`
 "enumeration" for inverse wavelet transform

The documentation for this class was generated from the following file:
• lift/liftbase.java

Generated on Sun Dec 11 20:01:10 2005 for LiftingScheme by  1.4.5