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Diffstat (limited to 'src/main/java/org/apache/commons/math3/transform/DctNormalization.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/transform/DctNormalization.java | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/transform/DctNormalization.java b/src/main/java/org/apache/commons/math3/transform/DctNormalization.java new file mode 100644 index 0000000..2f38d04 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/transform/DctNormalization.java @@ -0,0 +1,62 @@ +/* + * 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>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)], + * </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>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)], + * </ul> + * + * which makes the transform orthogonal. N is the size of the data sample. + */ + ORTHOGONAL_DCT_I; +} |