/*
* 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 Also: - FastCosineTransformer
Since: 3.0
/**
* 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 FastCosineTransformer to use the standard normalization convention. The standard
DCT-I normalization convention is defined as follows
- forward transform:
yn = (1/2) [x0 + (-1)nxN-1]
+ ∑k=1N-2
xk cos[π nk / (N - 1)],
- inverse transform:
xk = [1 / (N - 1)] [y0
+ (-1)kyN-1]
+ [2 / (N - 1)] ∑n=1N-2
yn cos[π nk / (N - 1)],
where N is the size of the data sample.
/**
* 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 FastCosineTransformer to use the orthogonal normalization convention. The orthogonal
DCT-I normalization convention is defined as follows
- forward transform:
yn = [2(N - 1)]-1/2 [x0
+ (-1)nxN-1]
+ [2 / (N - 1)]1/2 ∑k=1N-2
xk cos[π nk / (N - 1)],
- inverse transform:
xk = [2(N - 1)]-1/2 [y0
+ (-1)kyN-1]
+ [2 / (N - 1)]1/2 ∑n=1N-2
yn cos[π nk / (N - 1)],
which makes the transform orthogonal. N is the size of the data sample.
/**
* 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;
}