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 */
017package org.apache.commons.math4.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 * @since 3.0
026 */
027public enum DctNormalization {
028    /**
029     * Should be passed to the constructor of {@link FastCosineTransformer}
030     * to use the <em>standard</em> normalization convention.  The standard
031     * DCT-I normalization convention is defined as follows
032     * <ul>
033     * <li>forward transform:
034     * y<sub>n</sub> = (1/2) [x<sub>0</sub> + (-1)<sup>n</sup>x<sub>N-1</sub>]
035     * + &sum;<sub>k=1</sub><sup>N-2</sup>
036     * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
037     * <li>inverse transform:
038     * x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub>
039     * + (-1)<sup>k</sup>y<sub>N-1</sub>]
040     * + [2 / (N - 1)] &sum;<sub>n=1</sub><sup>N-2</sup>
041     * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
042     * </ul>
043     * where N is the size of the data sample.
044     */
045    STANDARD_DCT_I,
046
047    /**
048     * Should be passed to the constructor of {@link FastCosineTransformer}
049     * to use the <em>orthogonal</em> normalization convention. The orthogonal
050     * DCT-I normalization convention is defined as follows
051     * <ul>
052     * <li>forward transform:
053     * y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub>
054     * + (-1)<sup>n</sup>x<sub>N-1</sub>]
055     * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>k=1</sub><sup>N-2</sup>
056     * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
057     * <li>inverse transform:
058     * x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub>
059     * + (-1)<sup>k</sup>y<sub>N-1</sub>]
060     * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>n=1</sub><sup>N-2</sup>
061     * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
062     * </ul>
063     * which makes the transform orthogonal. N is the size of the data sample.
064     */
065    ORTHOGONAL_DCT_I;
066}