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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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 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.
*/
STANDARD_DCT_I,
/**
* Should be passed to the constructor of {@link 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.
*/
ORTHOGONAL_DCT_I;
}