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 }