| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math3.transform; |
| |
| /** |
| * This enumeration defines the various types of normalizations that can be |
| * applied to discrete cosine transforms (DCT). The exact definition of these |
| * normalizations is detailed below. |
| * |
| * @see FastCosineTransformer |
| * @since 3.0 |
| */ |
| public enum DctNormalization { |
| /** |
| * Should be passed to the constructor of {@link FastCosineTransformer} |
| * to use the <em>standard</em> normalization convention. The standard |
| * DCT-I normalization convention is defined as follows |
| * <ul> |
| * <li>forward transform: |
| * y<sub>n</sub> = (1/2) [x<sub>0</sub> + (-1)<sup>n</sup>x<sub>N-1</sub>] |
| * + ∑<sub>k=1</sub><sup>N-2</sup> |
| * x<sub>k</sub> cos[π nk / (N - 1)],</li> |
| * <li>inverse transform: |
| * x<sub>k</sub> = [1 / (N - 1)] [y<sub>0</sub> |
| * + (-1)<sup>k</sup>y<sub>N-1</sub>] |
| * + [2 / (N - 1)] ∑<sub>n=1</sub><sup>N-2</sup> |
| * y<sub>n</sub> cos[π nk / (N - 1)],</li> |
| * </ul> |
| * where N is the size of the data sample. |
| */ |
| STANDARD_DCT_I, |
| |
| /** |
| * Should be passed to the constructor of {@link FastCosineTransformer} |
| * to use the <em>orthogonal</em> normalization convention. The orthogonal |
| * DCT-I normalization convention is defined as follows |
| * <ul> |
| * <li>forward transform: |
| * y<sub>n</sub> = [2(N - 1)]<sup>-1/2</sup> [x<sub>0</sub> |
| * + (-1)<sup>n</sup>x<sub>N-1</sub>] |
| * + [2 / (N - 1)]<sup>1/2</sup> ∑<sub>k=1</sub><sup>N-2</sup> |
| * x<sub>k</sub> cos[π nk / (N - 1)],</li> |
| * <li>inverse transform: |
| * x<sub>k</sub> = [2(N - 1)]<sup>-1/2</sup> [y<sub>0</sub> |
| * + (-1)<sup>k</sup>y<sub>N-1</sub>] |
| * + [2 / (N - 1)]<sup>1/2</sup> ∑<sub>n=1</sub><sup>N-2</sup> |
| * y<sub>n</sub> cos[π nk / (N - 1)],</li> |
| * </ul> |
| * which makes the transform orthogonal. N is the size of the data sample. |
| */ |
| ORTHOGONAL_DCT_I; |
| } |