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> = ∑<sub>k=0</sub><sup>N-1</sup> 035 * x<sub>k</sub> exp(-2πi n k / N),</li> 036 * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup> 037 * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi 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 / √N) 049 * ∑<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub> 050 * exp(-2πi n k / N),</li> 051 * <li>inverse transform: x<sub>k</sub> = (1 / √N) 052 * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi n k / N),</li> 053 * </ul> 054 * which makes the transform unitary. N is the size of the data sample. 055 */ 056 UNITARY; 057 }