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 sine transforms (DST). The exact definition of these
022 * normalizations is detailed below.
023 *
024 * @see FastSineTransformer
025 * @since 3.0
026 */
027public enum DstNormalization {
028    /**
029     * Should be passed to the constructor of {@link FastSineTransformer} to
030     * use the <em>standard</em> normalization convention. The standard DST-I
031     * normalization convention is defined as follows
032     * <ul>
033     * <li>forward transform: y<sub>n</sub> = &sum;<sub>k=0</sub><sup>N-1</sup>
034     * x<sub>k</sub> sin(&pi; nk / N),</li>
035     * <li>inverse transform: x<sub>k</sub> = (2 / N)
036     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> sin(&pi; nk / N),</li>
037     * </ul>
038     * where N is the size of the data sample, and x<sub>0</sub> = 0.
039     */
040    STANDARD_DST_I,
041
042    /**
043     * Should be passed to the constructor of {@link FastSineTransformer} to
044     * use the <em>orthogonal</em> normalization convention. The orthogonal
045     * DCT-I normalization convention is defined as follows
046     * <ul>
047     * <li>Forward transform: y<sub>n</sub> = &radic;(2 / N)
048     * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub> sin(&pi; nk / N),</li>
049     * <li>Inverse transform: x<sub>k</sub> = &radic;(2 / N)
050     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> sin(&pi; nk / N),</li>
051     * </ul>
052     * which makes the transform orthogonal. N is the size of the data sample,
053     * and x<sub>0</sub> = 0.
054     */
055    ORTHOGONAL_DST_I
056}