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 * + ∑<sub>k=1</sub><sup>N-2</sup>
40 * x<sub>k</sub> cos[π 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)] ∑<sub>n=1</sub><sup>N-2</sup>
45 * y<sub>n</sub> cos[π 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> ∑<sub>k=1</sub><sup>N-2</sup>
60 * x<sub>k</sub> cos[π 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> ∑<sub>n=1</sub><sup>N-2</sup>
65 * y<sub>n</sub> cos[π 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 }