| /* |
| * 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.math4.transform; |
| |
| /** |
| * This enumeration defines the various types of normalizations that can be |
| * applied to discrete Fourier transforms (DFT). The exact definition of these |
| * normalizations is detailed below. |
| * |
| * @see FastFourierTransformer |
| * @since 3.0 |
| */ |
| public enum DftNormalization { |
| /** |
| * Should be passed to the constructor of {@link FastFourierTransformer} |
| * to use the <em>standard</em> normalization convention. This normalization |
| * convention is defined as follows |
| * <ul> |
| * <li>forward transform: y<sub>n</sub> = ∑<sub>k=0</sub><sup>N-1</sup> |
| * x<sub>k</sub> exp(-2πi n k / N),</li> |
| * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup> |
| * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi n k / N),</li> |
| * </ul> |
| * where N is the size of the data sample. |
| */ |
| STANDARD, |
| |
| /** |
| * Should be passed to the constructor of {@link FastFourierTransformer} |
| * to use the <em>unitary</em> normalization convention. This normalization |
| * convention is defined as follows |
| * <ul> |
| * <li>forward transform: y<sub>n</sub> = (1 / √N) |
| * ∑<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub> |
| * exp(-2πi n k / N),</li> |
| * <li>inverse transform: x<sub>k</sub> = (1 / √N) |
| * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi n k / N),</li> |
| * </ul> |
| * which makes the transform unitary. N is the size of the data sample. |
| */ |
| UNITARY; |
| } |