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haar_classicFreq Class Template Reference

haar_classicFreq. More...

#include <haar_classicFreq.h>

Inheritance diagram for haar_classicFreq::

haar_classic liftbase List of all members.

Public Methods

void forwardStepRev (T &vec, const int n)
 One forward step of the reverse Haar classic transform, where the results for the high and low pass filters are reversed. More...

void inverseStepRev (T &vec, const int n)
 One inverse step of the reverse Haar classic transform, where the results for the high and low pass filters are reversed. More...


Protected Methods

void predictRev (T &vec, int N, transDirection direction)
 In the standard wavelet transform, the high pass filter is applied to the upper half of the array (this is the predict phase, in lifting scheme terminology). More...

void updateRev (T &vec, int N, transDirection direction)
 Reverse low pass filter. More...

Detailed Description

template<class T> class haar_classicFreq

haar_classicFreq.

An extension of the "Haar classic" algorithm for frequency analysis.

The haar_classicFreq template extends the haar_classic templace. The haar_classic template implements what I call the "Haar classic" algorithm. Here the high pass filter (wavelet) is 

     b'i = (ai - bi)/2

where ai is an even element and bi is it odd element neighbor (of course using a lifting scheme style implementation, the even elements are moved to the first half of the array and the odd elements are moved to the second half.

In the Haar classic algorithm the high pass result is placed in the upper half of the array. In the haar_classicFreq version the result is placed in the lower half of the array and the equation becomes 

     a'i = (ai - bi)/2

The "Haar classic" low pass filter (smoothing function) is 

     a'i = (ai + bi)/2

In the Haar classic algorithm the low pass filter result is placed in the lower half of the array. In the haar_classicFreq version the result is placed in the upper half of the array and the equation becomes 

     b'i = (ai + bi)/2

The calculation of the high pass filter is done first and overwrites the even elements (e.g., a'i). To recover the ai values given a'i and bi: 

     a'i = (ai - bi)/2
     2 * a'i = ai - bi
     ai = 2 * a'i + bi

Substituting this into the equation for calculating b'i we get: 

     b'i = ((2 * a'i + bi) + bi)/2
     b'i = (2 * a'i + 2 * bi)/2
     b'i = a'i + bi

These equations differ from the Haar classic forward transform equations.

Author:
Ian Kaplan

Definition at line 79 of file haar_classicFreq.h.

Member Function Documentation

template<class T>
void haar_classicFreq<T>::forwardStepRev ( T & vec,
const int n ) [inline, virtual]
 

One forward step of the reverse Haar classic transform, where the results for the high and low pass filters are reversed.

Reimplemented from liftbase.

Definition at line 154 of file haar_classicFreq.h.

00155   {
00156     split( vec, n ); 
00157     predictRev( vec, n, forward );
00158     updateRev( vec, n, forward );
00159   }

template<class T>
void haar_classicFreq<T>::inverseStepRev ( T & vec,
const int n ) [inline, virtual]
 

One inverse step of the reverse Haar classic transform, where the results for the high and low pass filters are reversed.

Reimplemented from liftbase.

Definition at line 167 of file haar_classicFreq.h.

00168   {
00169     updateRev( vec, n, inverse );
00170     predictRev( vec, n, inverse );
00171     merge( vec, n );
00172   }

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

In the standard wavelet transform, the high pass filter is applied to the upper half of the array (this is the predict phase, in lifting scheme terminology).

In the reverse transform step, which is used for wavelet frequency analysis, the high pass filter is applied to the lower half of the array.

Reimplemented from liftbase.

Definition at line 92 of file haar_classicFreq.h.

00093   {
00094     int half = N >> 1;
00095     int cnt = 0;
00096 
00097     for (int i = 0; i < half; i++) {
00098       int j = i + half;
00099 
00100       if (direction == forward) {
00101         vec[i] = (vec[i] - vec[j] )/2;
00102       }
00103       else if (direction == inverse) {
00104         vec[i] =  (2 * vec[i]) + vec[j];
00105       }
00106       else {
00107         printf("predictRev: bad direction value\n");
00108       }
00109     }
00110   } // predictRev

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

Reverse low pass filter.

In the standard wavelet transform the low pass filter is applied to the data set (consisting of N elements) and the result is placed in the lower half of the array (the lower N/2 elements).

In the reverse transform step, which is used for wavelet frequency analysis, the result of the low pass filter is placed in the upper half of the array (the upper N/2 elements).

Reimplemented from liftbase.

Definition at line 127 of file haar_classicFreq.h.

00128   {
00129     int half = N >> 1;
00130 
00131     for (int i = 0; i < half; i++) {
00132       int j = i + half;
00133 
00134       if (direction == forward) {
00135         vec[j] = vec[j] + vec[i];
00136       }
00137       else if (direction == inverse) {
00138         vec[j] = vec[j] - vec[i];
00139       }
00140       else {
00141         printf("updateRev: bad direction value\n");
00142       }
00143     }
00144   } // updateRev

The documentation for this class was generated from the following file:
Generated at Sat Aug 10 13:23:37 2002 for Wavelet Packet Transform and Lossless Compression by doxygen1.2.8.1 written by Dimitri van Heesch, © 1997-2001