fastfouriertransformer.java

Apache的common math数学软件包

/*
 * 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.math.transform;

import java.io.Serializable;
import org.apache.commons.math.analysis.*;
import org.apache.commons.math.complex.*;
import org.apache.commons.math.MathException;

/**
 * Implements the <a href="http://mathworld.wolfram.com/FastFourierTransform.html">
 * Fast Fourier Transform</a> for transformation of one-dimensional data sets.
 * For reference, see <b>Applied Numerical Linear Algebra</b>, ISBN 0898713897,
 * chapter 6.
 * <p>
 * There are several conventions for the definition of FFT and inverse FFT,
 * mainly on different coefficient and exponent. Here the equations are listed
 * in the comments of the corresponding methods.</p>
 * <p>
 * We require the length of data set to be power of 2, this greatly simplifies
 * and speeds up the code. Users can pad the data with zeros to meet this
 * requirement. There are other flavors of FFT, for reference, see S. Winograd,
 * <i>On computing the discrete Fourier transform</i>, Mathematics of Computation,
 * 32 (1978), 175 - 199.</p>
 *
 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
 * @since 1.2
 */
public class FastFourierTransformer implements Serializable {

    /** serializable version identifier */
    static final long serialVersionUID = 5138259215438106000L;

    /** array of the roots of unity */
    private Complex omega[] = new Complex[0];

    /**
     * |omegaCount| is the length of lasted computed omega[]. omegaCount
     * is positive for forward transform and negative for inverse transform.
     */
    private int omegaCount = 0;

    /**
     * Construct a default transformer.
     */
    public FastFourierTransformer() {
        super();
    }

    /**
     * Transform the given real data set.
     * <p>
     * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
     * </p>
     * 
     * @param f the real data array to be transformed
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform(double f[]) throws MathException,
        IllegalArgumentException {

        return fft(f, false);
    }

    /**
     * Transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
     * </p>
     * 
     * @param f the function to be sampled and transformed
     * @param min the lower bound for the interval
     * @param max the upper bound for the interval
     * @param n the number of sample points
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, IllegalArgumentException {

        double data[] = sample(f, min, max, n);
        return fft(data, false);
    }

    /**
     * Transform the given complex data set.
     * <p>
     * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $
     * </p>
     * 
     * @param f the complex data array to be transformed
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform(Complex f[]) throws MathException,
        IllegalArgumentException {

        computeOmega(f.length);
        return fft(f);
    }

    /**
     * Transform the given real data set.
     * <p>
     * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
     * </p>
     * 
     * @param f the real data array to be transformed
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform2(double f[]) throws MathException,
        IllegalArgumentException {

        double scaling_coefficient = 1.0 / Math.sqrt(f.length);
        return scaleArray(fft(f, false), scaling_coefficient);
    }

    /**
     * Transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
     * </p>
     * 
     * @param f the function to be sampled and transformed
     * @param min the lower bound for the interval
     * @param max the upper bound for the interval
     * @param n the number of sample points
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform2(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, IllegalArgumentException {

        double data[] = sample(f, min, max, n);
        double scaling_coefficient = 1.0 / Math.sqrt(n);
        return scaleArray(fft(data, false), scaling_coefficient);
    }

    /**
     * Transform the given complex data set.
     * <p>
     * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$
     * </p>
     * 
     * @param f the complex data array to be transformed
     * @return the complex transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] transform2(Complex f[]) throws MathException,
        IllegalArgumentException {

        computeOmega(f.length);
        double scaling_coefficient = 1.0 / Math.sqrt(f.length);
        return scaleArray(fft(f), scaling_coefficient);
    }

    /**
     * Inversely transform the given real data set.
     * <p>
     * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
     * </p>
     * 
     * @param f the real data array to be inversely transformed
     * @return the complex inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] inversetransform(double f[]) throws MathException,
        IllegalArgumentException {

        double scaling_coefficient = 1.0 / f.length;
        return scaleArray(fft(f, true), scaling_coefficient);
    }

    /**
     * Inversely transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
     * </p>
     * 
     * @param f the function to be sampled and inversely transformed
     * @param min the lower bound for the interval
     * @param max the upper bound for the interval
     * @param n the number of sample points
     * @return the complex inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] inversetransform(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, IllegalArgumentException {

        double data[] = sample(f, min, max, n);
        double scaling_coefficient = 1.0 / n;
        return scaleArray(fft(data, true), scaling_coefficient);
    }

    /**
     * Inversely transform the given complex data set.
     * <p>
     * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $
     * </p>
     * 
     * @param f the complex data array to be inversely transformed
     * @return the complex inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] inversetransform(Complex f[]) throws MathException,
        IllegalArgumentException {

        computeOmega(-f.length);    // pass negative argument
        double scaling_coefficient = 1.0 / f.length;
        return scaleArray(fft(f), scaling_coefficient);
    }

    /**
     * Inversely transform the given real data set.
     * <p>
     * The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$
     * </p>
     * 
     * @param f the real data array to be inversely transformed
     * @return the complex inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] inversetransform2(double f[]) throws MathException,
        IllegalArgumentException {

        double scaling_coefficient = 1.0 / Math.sqrt(f.length);
        return scaleArray(fft(f, true), scaling_coefficient);
    }

    /**
     * Inversely transform the given real function, sampled on the given interval.
     * <p>
     * The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$
     * </p>
     * 
     * @param f the function to be sampled and inversely transformed
     * @param min the lower bound for the interval
     * @param max the upper bound for the interval
     * @param n the number of sample points
     * @return the complex inversely transformed array
     * @throws MathException if any math-related errors occur
     * @throws IllegalArgumentException if any parameters are invalid
     */
    public Complex[] inversetransform2(
        UnivariateRealFunction f, double min, double max, int n)
        throws MathException, IllegalArgumentException {

        double data[] = sample(f, min, max, n);
        double scaling_coefficient = 1.0 / Math.sqrt(n);
        return scaleArray(fft(data, true), scaling_coefficient);
    }

    /**
     * Inversely transform the given complex data set.