写一段傅里叶变换算法的java代码

### 回答1：
傅里叶变换是用来对一个信号进行频率分析的算法。下面是一段使用Java实现的傅里叶变换的代码示例：

import java.util.ArrayList;
import java.util.List;
import java.util.function.Function;

public class FFT {
    private final int N;
    private final List<Complex> roots;
    private final Function<Complex, Complex> inverse;

    public FFT(int n, boolean inverse) {
        this.N = n;
        this.roots = roots(n, inverse);
        this.inverse = inverse ? Complex::conjugate : Function.identity();
    }

    public List<Complex> apply(List<Complex> a) {
        int n = a.size();
        if (n != N) {
            throw new IllegalArgumentException("Size mismatch");
        }
        if (n == 1) {
            return a;
        }
        List<Complex> even = new ArrayList<>(n / 2);
        List<Complex> odd = new ArrayList<>(n / 2);
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                even.add(a.get(i));
            } else {
                odd.add(a.get(i));
            }
        }
        List<Complex> q = apply(even);
        List<Complex> r = apply(odd);
        List<Complex> y = new ArrayList<>(n);
        for (int k = 0; k < n / 2; k++) {
            Complex z = roots.get(k).multiply(r.get(k));
            y.add(q.get(k).add(z));
            y.add(q.get(k).subtract(z));
        }
        return y;
    }

    public static List<Complex> roots(int n, boolean inverse) {
        List<Complex> roots = new ArrayList<>(n / 2);
        double angle = 2 * Math.PI / n * (inverse ? -1 : 1);
        for (int k = 0; k < n / 2; k++) {
            roots.add(Complex.fromPolar(1, angle * k));
        }
        return roots;
    }
}

class Complex {
    final double re;
    final double im;

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

    public static Complex fromPolar(double r, double theta) {
        return new Complex(r * Math.cos(theta), r * Math.sin(theta));
    }

    public double re() {
        return re;
    }

    public double im() {
        return im;
    }

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

    public Complex add  

### 回答2：
傅里叶变换是信号处理领域中常用的算法，可将时域信号转换为频域信号。以下是一个简单的傅里叶变换算法的Java代码示例：

import java.util.Arrays;

public class FourierTransform {
// 傅里叶变换算法
public static Complex[] fft(Complex[] x) {
int N = x.length;

// 基本情况，如果输入只有一个元素，则直接返回
if (N == 1) {
return new Complex[] { x[0] };
}

// 创建偶数索引和奇数索引的数组
Complex[] even = new Complex[N / 2];
Complex[] odd = new Complex[N / 2];
for (int k = 0; k < N / 2; k++) {
even[k] = x[2 * k];
odd[k] = x[2 * k + 1];
}

// 递归计算偶数索引和奇数索引的傅里叶变换
Complex[] q = fft(even);
Complex[] r = fft(odd);

// 合并两个结果
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[] { new Complex(1, 0), new Complex(2, 0), new Complex(3, 0), new Complex(4, 0) };

// 调用傅里叶变换算法
Complex[] y = fft(x);

System.out.println("输入信号：");
System.out.println(Arrays.toString(x));

System.out.println("傅里叶变换结果：");
System.out.println(Arrays.toString(y));
}
}

class Complex {
private final double real;
private final double imag;

public Complex(double real, double imag) {
this.real = real;
this.imag = imag;
}

public Complex plus(Complex other) {
double real = this.real + other.real;
double imag = this.imag + other.imag;
return new Complex(real, imag);
}

public Complex minus(Complex other) {
double real = this.real - other.real;
double imag = this.imag - other.imag;
return new Complex(real, imag);
}

public Complex times(Complex other) {
double real = this.real * other.real - this.imag * other.imag;
double imag = this.real * other.imag + this.imag * other.real;
return new Complex(real, imag);
}

@Override
public String toString() {
return "(" + real + ", " + imag + ")";
}
}

以上代码实现了一个简单的傅里叶变换算法，在`fft()`方法中，使用递归将输入数组分成偶数和奇数索引两个子数组，分别对其进行傅里叶变换，然后合并两个结果，最终得到傅里叶变换结果。代码中使用的`Complex`类用于表示复数，并实现了复数的加、减、乘等运算。在`main()`方法中，首先创建一个复数数组作为输入信号，然后调用傅里叶变换算法计算结果，最后输出结果。