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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
22  package org.hipparchus.transform;
23  
24  /**
25   * This enumeration defines the various types of normalizations that can be
26   * applied to discrete cosine transforms (DCT). The exact definition of these
27   * normalizations is detailed below.
28   *
29   * @see FastCosineTransformer
30   */
31  public enum DctNormalization {
32      /**
33       * Should be passed to the constructor of {@link FastCosineTransformer}
34       * to use the <em>standard</em> normalization convention.  The standard
35       * DCT-I normalization convention is defined as follows
36       * <ul>
37       * <li>forward transform:
38       * y<sub>n</sub> = (1/2) [x<sub>0</sub> + (-1)<sup>n</sup>x<sub>N-1</sub>]
39       * + &sum;<sub>k=1</sub><sup>N-2</sup>
40       * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
41       * <li>inverse transform:
42       * x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub>
43       * + (-1)<sup>k</sup>y<sub>N-1</sub>]
44       * + [2 / (N - 1)] &sum;<sub>n=1</sub><sup>N-2</sup>
45       * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
46       * </ul>
47       * where N is the size of the data sample.
48       */
49      STANDARD_DCT_I,
50  
51      /**
52       * Should be passed to the constructor of {@link FastCosineTransformer}
53       * to use the <em>orthogonal</em> normalization convention. The orthogonal
54       * DCT-I normalization convention is defined as follows
55       * <ul>
56       * <li>forward transform:
57       * y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub>
58       * + (-1)<sup>n</sup>x<sub>N-1</sub>]
59       * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>k=1</sub><sup>N-2</sup>
60       * x<sub>k</sub> cos[&pi; nk / (N - 1)],</li>
61       * <li>inverse transform:
62       * x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub>
63       * + (-1)<sup>k</sup>y<sub>N-1</sub>]
64       * + [2 / (N - 1)]<sup>1/2</sup> &sum;<sub>n=1</sub><sup>N-2</sup>
65       * y<sub>n</sub> cos[&pi; nk / (N - 1)],</li>
66       * </ul>
67       * which makes the transform orthogonal. N is the size of the data sample.
68       */
69      ORTHOGONAL_DCT_I;
70  }