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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 Also:
FastFourierTransformer
Since:
3.0/**
 * 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 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.
/**
     * 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> = &sum;<sub>k=0</sub><sup>N-1</sup>
     * x<sub>k</sub> exp(-2&pi;i n k / N),</li>
     * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup>
     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
     * </ul>
     * where N is the size of the data sample.
     */
    STANDARD,

    
Should be passed to the constructor of 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.
/**
     * 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 / &radic;N)
     * &sum;<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub>
     * exp(-2&pi;i n k / N),</li>
     * <li>inverse transform: x<sub>k</sub> = (1 / &radic;N)
     * &sum;<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2&pi;i n k / N),</li>
     * </ul>
     * which makes the transform unitary. N is the size of the data sample.
     */
    UNITARY;
}