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 Fourier transforms (DFT). The exact definition of these
022 * normalizations is detailed below.
023 *
024 * @see FastFourierTransformer
025 * @since 3.0
026 */
027public enum DftNormalization {
028    /**
029     * Should be passed to the constructor of {@link FastFourierTransformer}
030     * to use the <em>standard</em> normalization convention. This normalization
031     * 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> exp(-2&pi;i n k / N),</li>
035     * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup>
036     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
037     * </ul>
038     * where N is the size of the data sample.
039     */
040    STANDARD,
041
042    /**
043     * Should be passed to the constructor of {@link FastFourierTransformer}
044     * to use the <em>unitary</em> normalization convention. This normalization
045     * convention is defined as follows
046     * <ul>
047     * <li>forward transform: y<sub>n</sub> = (1 / &radic;N)
048     * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub>
049     * exp(-2&pi;i n k / N),</li>
050     * <li>inverse transform: x<sub>k</sub> = (1 / &radic;N)
051     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
052     * </ul>
053     * which makes the transform unitary. N is the size of the data sample.
054     */
055    UNITARY;
056}