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/*
 * 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
 *
 *      https://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.
 */

/*
 * This is not the original file distributed by the Apache Software Foundation
 * It has been modified by the Hipparchus project
 */
package org.hipparchus.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
 */
public enum DftNormalization {
    /**
     * Should be passed to the constructor of {@link FastFourierTransformer}
     * to use the standard normalization convention. This normalization
     * convention is defined as follows
     * 
     * forward transform: y_n = ∑_k=0^N-1
     * x_k exp(-2πi n k / N),
     * inverse transform: x_k = N^-1
     * ∑_n=0^N-1 y_n exp(2πi n k / N),
     * 
     * where N is the size of the data sample.
     */
    STANDARD,

    /**
     * Should be passed to the constructor of {@link FastFourierTransformer}
     * to use the unitary normalization convention. This normalization
     * convention is defined as follows
     * 
     * forward transform: y_n = (1 / √N)
     * ∑_k=0^N-1 x_k
     * exp(-2πi n k / N),
     * inverse transform: x_k = (1 / √N)
     * ∑_n=0^N-1 y_n exp(2πi n k / N),
     * 
     * which makes the transform unitary. N is the size of the data sample.
     */
    UNITARY
}