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 Fourier transforms (DFT). The exact definition of these
022     * normalizations is detailed below.
023     *
024     * @see FastFourierTransformer
025     * @version $Id: DftNormalization.java 1385310 2012-09-16 16:32:10Z tn $
026     * @since 3.0
027     */
028    public enum DftNormalization {
029        /**
030         * Should be passed to the constructor of {@link FastFourierTransformer}
031         * to use the <em>standard</em> normalization convention. This normalization
032         * convention is defined as follows
033         * <ul>
034         * <li>forward transform: y<sub>n</sub> = &sum;<sub>k=0</sub><sup>N-1</sup>
035         * x<sub>k</sub> exp(-2&pi;i n k / N),</li>
036         * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup>
037         * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
038         * </ul>
039         * where N is the size of the data sample.
040         */
041        STANDARD,
042    
043        /**
044         * Should be passed to the constructor of {@link FastFourierTransformer}
045         * to use the <em>unitary</em> normalization convention. This normalization
046         * convention is defined as follows
047         * <ul>
048         * <li>forward transform: y<sub>n</sub> = (1 / &radic;N)
049         * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub>
050         * exp(-2&pi;i n k / N),</li>
051         * <li>inverse transform: x<sub>k</sub> = (1 / &radic;N)
052         * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
053         * </ul>
054         * which makes the transform unitary. N is the size of the data sample.
055         */
056        UNITARY;
057    }