Daub04.java

/**
 * JWave - Java implementation of wavelet transform algorithms
 *
 * Copyright 2010-2012 Christian Scheiblich
 *  
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at 
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License. 
 *
 * This file Daub04.java is part of JWave.
 *
 * @author Christian Scheiblich
 * date 26.03.2010 07:35:31
 * contact graetz@mailfish.de
 */
package math.transform.jwave.handlers.wavelets;

/**
 * Ingrid Daubechies' orthonormal wavelet of eight coefficients and the scales;
 * normed, due to ||*||2 - euclidean norm.
 * 
 * @date 26.03.2010 07:35:31
 * @author Christian Scheiblich
 */
public class Daub04 extends Wavelet {

  /**
   * Constructor setting up the orthonormal Daubechie6 wavelet coeffs and the
   * scales; normed, due to ||*||2 - euclidean norm.
   * 
   * @date 26.03.2010 07:35:31
   * @author Christian Scheiblich
   */
  public Daub04( ) {

    _waveLength = 8;

    _scales = new double[ _waveLength ];

    double sqrt02 = 1.4142135623730951;

    // TODO Get analytical formulation, due to its precision; this is around 1.e-3 only
    _scales[ 0 ] = 0.32580343; //  0.32580343
    _scales[ 1 ] = 1.01094572; //  1.01094572
    _scales[ 2 ] = 0.8922014; //  0.8922014
    _scales[ 3 ] = -0.03967503; // -0.03967503
    _scales[ 4 ] = -0.2645071; // -0.2645071
    _scales[ 5 ] = 0.0436163; //  0.0436163
    _scales[ 6 ] = 0.0465036; //  0.0465036
    _scales[ 7 ] = -0.01498699; // -0.01498699

    // normalize to square root of 2 for being orthonormal 
    for( int i = 0; i < _waveLength; i++ )
      _scales[ i ] /= sqrt02;

    _coeffs = new double[ _waveLength ];

    _coeffs[ 0 ] = _scales[ 7 ]; //  h7
    _coeffs[ 1 ] = -_scales[ 6 ]; // -h6
    _coeffs[ 2 ] = _scales[ 5 ]; //  h5
    _coeffs[ 3 ] = -_scales[ 4 ]; // -h4
    _coeffs[ 4 ] = _scales[ 3 ]; //  h3
    _coeffs[ 5 ] = -_scales[ 2 ]; // -h2
    _coeffs[ 6 ] = _scales[ 1 ]; //  h1
    _coeffs[ 7 ] = -_scales[ 0 ]; // -h0

  } // Daub04

} // class