java fft算法

Java中实现FFT算法可以使用JTransforms库。该库提供了快速的FFT实现，支持多种数据类型和维度的FFT计算。

以下是一个简单的示例代码：

import edu.emory.mathcs.jtransforms.fft.DoubleFFT_1D;

public class FFTExample {
    public static void main(String[] args) {
        double[] data = {1, 2, 3, 4, 5, 6, 7, 8};
        DoubleFFT_1D fft = new DoubleFFT_1D(data.length);
        fft.realForward(data);
        for (double d : data) {
            System.out.println(d);
        }
    }
}

相关问题

java实现FFT算法（附完整源码）

下面是Java实现FFT算法的代码：

import java.util.Arrays;

public class FFT {
    public static Complex[] fft(Complex[] x) {
        int N = x.length;

        // base case
        if (N == 1) return new Complex[] { x[0] };

        // radix 2 Cooley-Tukey FFT
        if (N % 2 != 0) {
            throw new RuntimeException("N is not a power of 2");
        }

        // fft of even terms
        Complex[] even = new Complex[N/2];
        for (int k = 0; k < N/2; k++) {
            even[k] = x[2*k];
        }
        Complex[] q = fft(even);

        // fft of odd terms
        Complex[] odd  = even;  // reuse the array
        for (int k = 0; k < N/2; k++) {
            odd[k] = x[2*k + 1];
        }
        Complex[] r = fft(odd);

        // combine
        Complex[] y = new Complex[N];
        for (int k = 0; k < N/2; k++) {
            double kth = -2 * k * Math.PI / N;
            Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
            y[k]       = q[k].plus(wk.times(r[k]));
            y[k + N/2] = q[k].minus(wk.times(r[k]));
        }
        return y;
    }

    public static void main(String[] args) { 
        Complex[] x = { new Complex(1, 0), new Complex(2, 0), new Complex(3, 0), new Complex(4, 0) };

        // FFT of original data
        Complex[] y = fft(x);

        // print results
        System.out.println("x");
        System.out.println("-------------------");
        for (int i = 0; i < x.length; i++) {
            System.out.println(x[i]);
        }
        System.out.println();

        System.out.println("y = fft(x)");
        System.out.println("-------------------");
        for (int i = 0; i < y.length; i++) {
            System.out.println(y[i]);
        }
        System.out.println();

        System.out.println("y = ifft(y)");
        System.out.println("-------------------");
        Complex[] z = ifft(y);
        for (int i = 0; i < z.length; i++) {
            System.out.println(z[i]);
        }
        System.out.println();
    }

    public static Complex[] ifft(Complex[] x) {
        int N = x.length;
        Complex[] y = new Complex[N];

        // take conjugate
        for (int i = 0; i < N; i++) {
            y[i] = x[i].conjugate();
        }

        // compute forward FFT
        y = fft(y);

        // take conjugate again
        for (int i = 0; i < N; i++) {
            y[i] = y[i].conjugate();
        }

        // divide by N
        for (int i = 0; i < N; i++) {
            y[i] = y[i].times(1.0 / N);
        }

        return y;
    }

}

class Complex {
    private final double re;   // the real part
    private final double im;   // the imaginary part

    // create a new object with the given real and imaginary parts
    public Complex(double real, double imag) {
        re = real;
        im = imag;
    }

    // return a string representation of the invoking Complex object
    public String toString() {
        if (im == 0) return re + "";
        if (re == 0) return im + "i";
        if (im <  0) return re + " - " + (-im) + "i";
        return re + " + " + im + "i";
    }

    // return abs/modulus/magnitude and angle/phase/argument
    public double abs()        { return Math.hypot(re, im); }  // Math.sqrt(re*re + im*im)
    public double phase()      { return Math.atan2(im, re); }  // between -pi and pi

    // return a new Complex object whose value is (this + b)
    public Complex plus(Complex b) {
        Complex a = this;             // invoking object
        double real = a.re + b.re;
        double imag = a.im + b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this - b)
    public Complex minus(Complex b) {
        Complex a = this;
        double real = a.re - b.re;
        double imag = a.im - b.im;
        return new Complex(real, imag);
    }

    // return a new Complex object whose value is (this * b)
    public Complex times(Complex b) {
        Complex a = this;
        double real = a.re * b.re - a.im * b.im;
        double imag = a.re * b.im + a.im * b.re;
        return new Complex(real, imag);
    }

    // scalar multiplication
    // return a new object whose value is (this * alpha)
    public Complex times(double alpha) {
        return new Complex(alpha * re, alpha * im);
    }

    // return a new Complex object whose value is the conjugate of this
    public Complex conjugate() {  return new Complex(re, -im); }

    // return a new Complex object whose value is the reciprocal of this
    public Complex reciprocal() {
        double scale = re*re + im*im;
        return new Complex(re / scale, -im / scale);
    }

    // return the real or imaginary part
    public double re() { return re; }
    public double im() { return im; }

    // return a / b
    public Complex divides(Complex b) {
        Complex a = this;
        return a.times(b.reciprocal());
    }

    // return a new Complex object whose value is the complex exponential of this
    public Complex exp() {
        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
    }

    // return a new Complex object whose value is the complex sine of this
    public Complex sin() {
        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex cosine of this
    public Complex cos() {
        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
    }

    // return a new Complex object whose value is the complex tangent of this
    public Complex tan() {
        return sin().divides(cos());
    }

    // a static version of plus
    public static Complex plus(Complex a, Complex b) {
        double real = a.re + b.re;
        double imag = a.im + b.im;
        Complex sum = new Complex(real, imag);
        return sum;
    }
}

上面的代码实现了FFT算法和IFFT算法，其中FFT算法使用递归实现，而IFFT算法则是在FFT算法的基础上进行了一些简单的变换。代码中用到了一个名为Complex的复数类，这里直接使用了作者提供的实现。

代码中的FFT算法输入为一个长度为2的n次方的复数数组，输出为进行了FFT变换后的复数数组；IFFT算法输入为一个进行了FFT变换后的复数数组，输出为进行了IFFT变换后的复数数组。

需要注意的是，这里的FFT算法只适用于输入长度为2的n次方的复数数组，输入长度不符合要求时会抛出异常。

java多项式相乘fft

FFT（快速傅里叶变换）是一种高效的算法，可用于多项式乘法。以下是Java中实现多项式相乘的FFT算法的代码示例：

import java.util.Arrays;

public class FFT {

    private Complex[] omega;

    public Complex[] fft(Complex[] A) {
        int n = A.length;

        if (n == 1)
            return new Complex[] { A[0] };

        Complex[] A0 = new Complex[n / 2];
        Complex[] A1 = new Complex[n / 2];
        for (int i = 0; i < n / 2; i++) {
            A0[i] = A[2 * i];
            A1[i] = A[2 * i + 1];
        }

        Complex[] y0 = fft(A0);
        Complex[] y1 = fft(A1);
        Complex[] y = new Complex[n];

        for (int k = 0; k < n / 2; k++) {
            Complex w = omega[n][k];
            y[k] = y0[k].plus(w.times(y1[k]));
            y[k + n / 2] = y0[k].minus(w.times(y1[k]));
        }

        return y;
    }

    public Complex[] inverseFFT(Complex[] y) {
        int n = y.length;

        Complex[] yInv = new Complex[n];
        for (int i = 0; i < n; i++) {
            yInv[i] = y[i].conjugate();
        }

        Complex[] aInv = fft(yInv);
        for (int i = 0; i < n; i++) {
            aInv[i] = aInv[i].conjugate().times(1.0 / n);
        }

        return aInv;
    }

    public void initOmega(int n) {
        omega = new Complex[n + 1];
        for (int i = 0; i <= n; i++) {
            double angle = 2 * Math.PI * i / n;
            omega[i] = new Complex(Math.cos(angle), Math.sin(angle));
        }
    }

    public Complex[] multiply(Complex[] a, Complex[] b) {
        int n = Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 1;
        initOmega(n);

        Complex[] A = Arrays.copyOf(a, n);
        Complex[] B = Arrays.copyOf(b, n);

        Complex[] y1 = fft(A);
        Complex[] y2 = fft(B);
        Complex[] y = new Complex[n];

        for (int k = 0; k < n; k++) {
            y[k] = y1[k].times(y2[k]);
        }

        Complex[] c = inverseFFT(y);
        return c;
    }

    public static void main(String[] args) {
        FFT fft = new FFT();
        Complex[] a = new Complex[] { new Complex(1), new Complex(2), new Complex(3) };
        Complex[] b = new Complex[] { new Complex(4), new Complex(5), new Complex(6) };
        Complex[] c = fft.multiply(a, b);

        for (int i = 0; i < c.length; i++) {
            System.out.print(c[i] + " ");
        }
    }
}

class Complex {
    public double re;
    public double im;

    public Complex(double re, double im) {
        this.re = re;
        this.im = im;
    }

    public Complex plus(Complex other) {
        return new Complex(re + other.re, im + other.im);
    }

    public Complex minus(Complex other) {
        return new Complex(re - other.re, im - other.im);
    }

    public Complex times(Complex other) {
        return new Complex(re * other.re - im * other.im, re * other.im + im * other.re);
    }

    public Complex conjugate() {
        return new Complex(re, -im);
    }

    public String toString() {
        return String.format("(%f,%f)", re, im);
    }
}

该代码使用Complex类来表示复数，实现了FFT算法和多项式相乘的操作。在主方法中，可以看到如何使用该类来计算多项式a和b的乘积。