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haar_classic Class Template Reference

A version of the classic Haar wavelet transform. More...

#include <haar_classic.h>

Inheritance diagram for haar_classic::

List of all members.

Protected Methods
void	predict (T &vec, int N, transDirection direction)
	Calculate the Haar wavelet or difference function (high pass filter). More...
void	update (T &vec, int N, transDirection direction)
	Calculate the smoothing or scaling function (low pass filter). More...

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Detailed Description

template<class T> class haar_classic

A version of the classic Haar wavelet transform.

This particular version of the Haar wavelet transform is frequently given as the definition for the Haar transform. This version differs from the lifting scheme version. In the case of the lifting scheme version of the Haar transform, the inverse transform is a mirror of the forward transform. The only difference is that the plus and minus operators are interchanged. This algorithm does not have this symmetry.

For a data set of N elements, a wavelet transform will calculate N/2 smoothed values and N/2 difference values. In wavelet terminology the smoothed values are calculated by the scaling function and the difference (or coefficient) values are calculated by the wavelet function.

This class implements one version of the Haar wavelet transform. This particular version is used in the chapter 8 of Ripples in Mathematics by Jensen and la Cour-Harbo to illustrate the wavelet packet transform. I have used it to verify my version of the wavelet packet algorithm.

In the description below, an element a_i is an even element and an element b_i is an odd element.

In this version of the Haar wavelet transform the scaling (or smoothing) function is

     s = (a + b)/2

The wavelet function is

     d = (a - b)/2

A lifting scheme expression is used in this implementation. Here the wavelet function is calculated first. The wavelet results overwrite the odd b_i values. This means that the smoothing function values must be calculated with the result of the wavelet function. To recover the value of b_i we use the expression

     b = a - 2d

     s = (a + (a - 2d))/2

     s = (2a - 2d)/2

     s = a - d

The lifting scheme terminology is maintained in the algorithm, although it does not fully apply.

This is a template version of the Haar wavelet. The template must be instantiated with an array or an object that acts like an array. Objects that act like arrays define the left hand side and right hand side index operators: [].

See www.bearcave.com for more information on wavelets and the wavelet lifting scheme.

Author:

Ian Kaplan

Definition at line 111 of file haar_classic.h.

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Member Function Documentation

template<class T> void haar_classic<T>::predict ( T & vec, int N, transDirection direction ) [inline, protected, virtual]

Calculate the Haar wavelet or difference function (high pass filter). Reimplemented from liftbase. Definition at line 119 of file haar_classic.h. { int half = N >> 1; int cnt = 0; for (int i = 0; i < half; i++) { double predictVal = vec[i]; int j = i + half; if (direction == forward) { vec[j] = (predictVal - vec[j] )/2; } else if (direction == inverse) { vec[j] = predictVal - (2 * vec[j]); } else { printf("haar_classic::predict: bad direction value\n"); } } } // predict

template<class T> void haar_classic<T>::update ( T & vec, int N, transDirection direction ) [inline, protected, virtual]

Calculate the smoothing or scaling function (low pass filter). Reimplemented from liftbase. Definition at line 145 of file haar_classic.h. { int half = N >> 1; for (int i = 0; i < half; i++) { int j = i + half; double updateVal = vec[j]; if (direction == forward) { vec[i] = vec[i] - updateVal; } else if (direction == inverse) { vec[i] = vec[i] + updateVal; } else { printf("update: bad direction value\n"); } } } // update

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The documentation for this class was generated from the following file:

• haar_classic.h

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