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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 Fourier transforms (DFT). The exact definition of these
27   * normalizations is detailed below.
28   *
29   * @see FastFourierTransformer
30   */
31  public enum DftNormalization {
32      /**
33       * Should be passed to the constructor of {@link FastFourierTransformer}
34       * to use the <em>standard</em> normalization convention. This normalization
35       * convention is defined as follows
36       * <ul>
37       * <li>forward transform: y<sub>n</sub> = &sum;<sub>k=0</sub><sup>N-1</sup>
38       * x<sub>k</sub> exp(-2&pi;i n k / N),</li>
39       * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup>
40       * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
41       * </ul>
42       * where N is the size of the data sample.
43       */
44      STANDARD,
45  
46      /**
47       * Should be passed to the constructor of {@link FastFourierTransformer}
48       * to use the <em>unitary</em> normalization convention. This normalization
49       * convention is defined as follows
50       * <ul>
51       * <li>forward transform: y<sub>n</sub> = (1 / &radic;N)
52       * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub>
53       * exp(-2&pi;i n k / N),</li>
54       * <li>inverse transform: x<sub>k</sub> = (1 / &radic;N)
55       * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
56       * </ul>
57       * which makes the transform unitary. N is the size of the data sample.
58       */
59      UNITARY
60  }