math.jwave.transforms

Class AncientEgyptianDecomposition

java.lang.Object

math.jwave.transforms.BasicTransform

math.jwave.transforms.AncientEgyptianDecomposition

public class AncientEgyptianDecomposition
extends BasicTransform

A wavelet transform method for arrays and signals of arbitrary lengths, even odd lengths. The array is decomposed in several parts of optimal lengths by applying the ancient Egyptian decomposition. Hereby, the array or signal is decomposed to the largest possible sub arrays of two the power of p. Afterwards each sub array is transformed forward and copied back to the discrete position of the input array. The reverse transform applies the same vice versa. In more detail the ancient Egyptian Multiplication can be easily explained by the following example: 42 = 2^5 + 2^3 + 2^1 = 32 + 8 + 2. However, an array or signal of odd length produces the smallest ancient Egyptian multiplier 2^0 which is actually 1. Therefore, the matching sub array or signal is untouched an the coefficient is actually the wavelet coefficient of wavelet space of level 0. For an "orthonormal" wavelet this holds. See: http://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication

Constructor Summary

Constructors

Constructor and Description
AncientEgyptianDecomposition(BasicTransform waveTransform) Constructor taking the

Method Summary

Modifier and Type	Method and Description
double[]	forward(double[] arrTime) This forward method decomposes the given array of arbitrary length to sub arrays while applying the ancient Egyptian decomposition.
double[]	reverse(double[] arrHilb) This reverse method awaits an array of arbitrary length in wavelet space keeping the wavelet already decomposed by the ancient Egyptian decomposition.

Methods inherited from class math.jwave.transforms.BasicTransform

forward, forward, forward, reverse, reverse, reverse

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

AncientEgyptianDecomposition

public AncientEgyptianDecomposition(BasicTransform waveTransform)

Constructor taking the

Method Detail

forward

public double[] forward(double[] arrTime)

This forward method decomposes the given array of arbitrary length to sub arrays while applying the ancient Egyptian decomposition. Each sub array is transformed by the selected basic transform and the resulting wavelet coefficients are copied back to their original discrete positions.

Specified by:

forward in class BasicTransform

Parameters:

arrTime - coefficients of 1-D time domain

Returns:

coefficients of 1-D frequency or Hilbert domain

See Also:

BasicTransform.forward(double[])

reverse

public double[] reverse(double[] arrHilb)

This reverse method awaits an array of arbitrary length in wavelet space keeping the wavelet already decomposed by the ancient Egyptian decomposition. Therefore, each of the existing sub arrays of length 2^p is reverse transformed by the selected basic transform and the resulting coefficients of time domain are copied back to their original discrete positions.

Specified by:

reverse in class BasicTransform

Parameters:

arrHilb - coefficients of 1-D frequency or Hilbert domain

Returns:

coefficients of 1-D time domain

See Also:

BasicTransform.reverse(double[])