    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    }