    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    }