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line_norm Class Template Reference

Normalized linear interpolation wavelet (see comment for the normalize function). More...

#include <line_norm.h>

Inheritance diagram for line_norm::

List of all members.

Protected Methods
void	normalize (T &vec, int N, transDirection direction)
	The normalization step assures that each step of the wavelet transform has the constant "energy" where energy is defined as. More...
void	inverseStep (T &vec, const int n)
	One inverse wavelet transform step, with normalization. More...
void	forwardStep (T &vec, const int n)
	One step in the forward wavelet transform, with normalization. More...

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Detailed Description

template<class T> class line_norm

Normalized linear interpolation wavelet (see comment for the normalize function).

Definition at line 13 of file line_norm.h.

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Member Function Documentation

template<class T> void line_norm<T>::forwardStep ( T & vec, const int n ) [inline, protected, virtual]

One step in the forward wavelet transform, with normalization. Reimplemented from liftbase. Definition at line 80 of file line_norm.h. { split( vec, n ); predict( vec, n, forward ); update( vec, n, forward ); normalize( vec, n, forward ); } // forwardStep

template<class T> void line_norm<T>::inverseStep ( T & vec, const int n ) [inline, protected, virtual]

One inverse wavelet transform step, with normalization. Reimplemented from liftbase. Definition at line 69 of file line_norm.h. { normalize( vec, n, inverse ); update( vec, n, inverse ); predict( vec, n, inverse ); merge( vec, n ); } // inverseStep

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

The normalization step assures that each step of the wavelet transform has the constant "energy" where energy is defined as. double energy = 0.0; for (int n = 0; n < N; n++) { energy = energy + (a[i] * a[i]); } See 5.2.1 of Ripples in Mathematics by Jensen and la Cour-Harbo The most common implementation of the Haar transform leaves out the normalization step, since it does not make much of a difference in many cases. However, in the case of the wavelet packet transform, many of the cost functions are squares, so normalization produces smaller wavelet values (although the scaling function values are larger). This may lead to a better wavelet packet result (e.g., a few large values and lots of small values). Normalization does have the disadvantage of destroying the averaging property of the Haar wavelet algorithm. That is, the final scaling factor is no longer the mean of the time series. Definition at line 44 of file line_norm.h. Referenced by forwardStep(), and inverseStep(). { const double sqrt2 = sqrt( 2.0 ); int half = N >> 1; for (int i = 0; i < half; i++) { int j = i + half; if (direction == forward) { vec[i] = sqrt2 * vec[i]; vec[j] = vec[j]/sqrt2; } else if (direction == inverse) { vec[i] = vec[i]/sqrt2; vec[j] = sqrt2 * vec[j]; } else { printf("normalize: bad direction value\n"); } } // for } // normalize

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

• line_norm.h

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