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• DftNormalization.java

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org.apache.commons.math3.transform.DftNormalization Maven / Gradle / Ivy

/*
 * 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 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 standard normalization convention. This normalization
     * convention is defined as follows
     * 

     * 
forward transform: yn = ∑k=0N-1
     * xk exp(-2πi n k / N),
     * 
inverse transform: xk = N-1
     * ∑n=0N-1 yn 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: yn = (1 / √N)
     * ∑k=0N-1 xk
     * exp(-2πi n k / N),
     * 
inverse transform: xk = (1 / √N)
     * ∑n=0N-1 yn exp(2πi n k / N),
     * 
     * which makes the transform unitary. N is the size of the data sample.
     */
    UNITARY;
}