001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.transform;
018    
019    /**
020     * This enumeration defines the various types of normalizations that can be
021     * applied to discrete cosine transforms (DCT). The exact definition of these
022     * normalizations is detailed below.
023     *
024     * @see FastCosineTransformer
025     * @version $Id: DctNormalization.java 1385310 2012-09-16 16:32:10Z tn $
026     * @since 3.0
027     */
028    public enum DctNormalization {
029        /**
030         * Should be passed to the constructor of {@link FastCosineTransformer}
031         * to use the <em>standard</em> normalization convention.  The standard
032         * DCT-I normalization convention is defined as follows
033         * <ul>
034         * <li>forward transform:
035         * y<sub>n</sub> = (1/2) [x<sub>0</sub> + (-1)<sup>n</sup>x<sub>N-1</sub>]
036         * + &sum;<sub>k=1</sub><sup>N-2</sup>
037         * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
038         * <li>inverse transform:
039         * x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub>
040         * + (-1)<sup>k</sup>y<sub>N-1</sub>]
041         * + [2 / (N - 1)] &sum;<sub>n=1</sub><sup>N-2</sup>
042         * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
043         * </ul>
044         * where N is the size of the data sample.
045         */
046        STANDARD_DCT_I,
047    
048        /**
049         * Should be passed to the constructor of {@link FastCosineTransformer}
050         * to use the <em>orthogonal</em> normalization convention. The orthogonal
051         * DCT-I normalization convention is defined as follows
052         * <ul>
053         * <li>forward transform:
054         * y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub>
055         * + (-1)<sup>n</sup>x<sub>N-1</sub>]
056         * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>k=1</sub><sup>N-2</sup>
057         * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
058         * <li>inverse transform:
059         * x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub>
060         * + (-1)<sup>k</sup>y<sub>N-1</sub>]
061         * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>n=1</sub><sup>N-2</sup>
062         * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
063         * </ul>
064         * which makes the transform orthogonal. N is the size of the data sample.
065         */
066        ORTHOGONAL_DCT_I;
067    }