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 cosine transforms (DCT). The exact definition of these 022 * normalizations is detailed below. 023 * 024 * @see FastCosineTransformer 025 * @version $Id: DctNormalization.java 1385310 2012-09-16 16:32:10Z tn $ 026 * @since 3.0 027 */ 028 public enum DctNormalization { 029 /** 030 * Should be passed to the constructor of {@link FastCosineTransformer} 031 * to use the <em>standard</em> normalization convention. The standard 032 * DCT-I normalization convention is defined as follows 033 * <ul> 034 * <li>forward transform: 035 * y<sub>n</sub> = (1/2) [x<sub>0</sub> + (-1)<sup>n</sup>x<sub>N-1</sub>] 036 * + ∑<sub>k=1</sub><sup>N-2</sup> 037 * x<sub>k</sub> cos[π nk / (N - 1)],</li> 038 * <li>inverse transform: 039 * x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub> 040 * + (-1)<sup>k</sup>y<sub>N-1</sub>] 041 * + [2 / (N - 1)] ∑<sub>n=1</sub><sup>N-2</sup> 042 * y<sub>n</sub> cos[π nk / (N - 1)],</li> 043 * </ul> 044 * where N is the size of the data sample. 045 */ 046 STANDARD_DCT_I, 047 048 /** 049 * Should be passed to the constructor of {@link FastCosineTransformer} 050 * to use the <em>orthogonal</em> normalization convention. The orthogonal 051 * DCT-I normalization convention is defined as follows 052 * <ul> 053 * <li>forward transform: 054 * y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub> 055 * + (-1)<sup>n</sup>x<sub>N-1</sub>] 056 * + [2 / (N - 1)]<sup>1/2</sup> ∑<sub>k=1</sub><sup>N-2</sup> 057 * x<sub>k</sub> cos[π nk / (N - 1)],</li> 058 * <li>inverse transform: 059 * x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub> 060 * + (-1)<sup>k</sup>y<sub>N-1</sub>] 061 * + [2 / (N - 1)]<sup>1/2</sup> ∑<sub>n=1</sub><sup>N-2</sup> 062 * y<sub>n</sub> cos[π nk / (N - 1)],</li> 063 * </ul> 064 * which makes the transform orthogonal. N is the size of the data sample. 065 */ 066 ORTHOGONAL_DCT_I; 067 }